Abstract:
The present invention allows market participants to exchange bundles of assets, including assets in different asset classes. A market participant may value the bundle as an entity, alleviating the need to attempt to attain a value objective in the aggregate by valuing and trading assets individually. A bundle of assets to be traded is entered, wherein proportions of each asset to be traded in units of a specified bundle size are provided by the market participant. Assets to be acquired by one market participant are matched against the same asset which other market participants are seeking to dispose. A market participant may enter multiple bundles, and may specify substitutability among bundles by entering one or more portfolio constraints. An exchange of bundled assets among market participants, in units of the bundles themselves is effected when the exchange satisfies a predetermined set of criteria.

Description:
CROSS-REFERENCE TO CO-PENDING APPLICATION 
   This Application is a continuation-in-part of application Ser. No. 08/992,647, filed Dec. 17, 1997, now U.S. Pat. No. 6,035,287, entitled A METHOD AND APPARATUS FOR BUNDLE ASSET TRADING. 

   TECHNICAL FIELD 
   The present invention relates to a method and apparatus for trading assets in bundles. 
   BACKGROUND INFORMATION 
   Data processing systems for the exchange of financial instruments and securities are old in the art. For example, the first subsystem to be employed in commercial practice was Instinet, which began operations in 1969. The Instinet system was a subject of U.S. Pat. No. 3,573,547 issued on Apr. 6, 1971. Instinet permits subscribers to engage in direct trading of securities among themselves on an anonymous basis. In effect, Instinet replaces the telephone and voice communications with communications conducted via the data processing system, with confirmations of trades being automatically transmitted to each party and to the appropriate clearing entity for settlement. 
   Other electronic data processing systems are exchange based order routing processors. For example, on the New York Stock Exchange (NYSE) is the Designated Order Turnaround System (or DOT) through which member firms transmit market and limit orders directly to the post where a security is traded, thereby dispensing with the messenger services of a floor broker. Limit orders are electronically filed while market orders are exposed to the (market) in front of the specialist&#39;s post, and executed either by a floor broker or the specialist. Automated data processing systems for small order execution exist in the dealer markets as well. 
   Regardless of the implementation, all such data processing systems for asset trading operate on an asset-by-asset basis. A trader (or a broker acting as his agent) may enter an order to acquire or dispose of a particular asset, or a portfolio of assets. In either case, individual transactions are consummated with respect to each of the assets individually. However, in many situations, a market participant does not necessarily derive value for a single asset, but for a basket of assets. In such a circumstance, the acquisition or disposition of assets on a asset-by-asset basis in order to obtain the basket of assets in the right proportion, and at the right price, may prove to be a complicated and time consuming task. 
   The market participant&#39;s problem is further exacerbated when the assets are within different asset classes. Here and throughout, the term asset is used in its broadest sense. An asset may be anything of value, and in a particular context, may be a commodity or other good, securities, or services, as well as money. To illustrate the problem, consider the supply chain problem as applied, for example, to cross docking operations. A typical instance of cross docking arises in the grocery trade. 
   In the grocery trade, goods are received from a multiplicity of producers and manufacturers for ultimate distribution in retail markets which are widely disbursed. A good flows to the grocer as a unitary item in bulk from the producer or manufacturer. These must then be broken into smaller unit sizes and distributed to the retail outlets, along with other goods from other manufacturers. Thus, the flow of goods from the producers must be warehoused and then redistributed. The facilities for warehousing and introduction of goods into a transportation stream for redistribution are the so-called cross docking facilities. 
   It is common practice to outsource the cross docking facilities and the transportation for redistribution. Thus, a grocer must acquire both the cross docking capacity and the transportation services to effect its objective, and these are acquired from different sources, that is, in a fragmented market. Moreover, the value of one of the two requirements is greatly diminished without the acquisition of the other. 
   The value to the grocer is in the aggregate, or basket, represented by the cross docking capacity and transportation service. In effect the price of one could be traded off against the other. If a ready means of cheap transportation is available, then the acquirer could afford to pay more for the cross docking capacity, or use a cross docking facility with wasted capacity, or vice versa. However, the fragmentation of the market for these services makes it difficult to implement such tradeoffs. An acquirer of the services would be better able to satisfy his requirements if he could obtain them as a bundle. Then he would only need to set the bundle price as his objective price. The bundle trading market would allocate price between the resources exchanged. Such a bundled trading mechanism also would squeeze out inefficiencies associated with the fragmented market for these resources. 
   A similar situation exists in the securities markets. A trader acquiring or disposing of a portfolio of equities may wish to hedge the acquisition or disposition by offsetting transactions in futures, options, or perhaps foreign currencies. The transactions implementing these acquisitions and dispositions take place in a fragmented market. The different assets are traded in different markets and the transactions may be displaced one from the other both in place and in time. Trading the assets individually in the fragmented market may lead to an overall loss with respect to the basket of assets due to market volatility. Thus, there is a need in the art for a method and apparatus for implementing a mechanism by which a market basket, or “bundle,” of assets may be exchanged among market participants. 
   SUMMARY OF THE INVENTION 
   The previously mentioned needs are addressed by the present invention in which market participants will be able to exchange among themselves, a combination of assets as a bundle. An electronic data processing system executing a trade matching mechanism provides the function of a market intermediary, recombining assets from different market participants such that the requirements of participants seeking to acquire a particular asset are satisfied by participants seeking to dispose of the same asset. 
   Market participants enter their asset bundles into the data processing system. The data processing system operates continuously and market participants can submit new trade orders, or bundles, or cancel open orders, at any time. The data processing system operates continuously to find matches in real-time. 
   Each bundle contains a plurality of assets to be exchanged. Bundles are specified in terms of a bundle size, and a set of values representing the proportions of each of the assets to be exchanged, in terms of the bundle size. Each bundle may contain a subset of assets which the market participant seeks to acquire, and a second subset of assets of which the market participant seeks to dispose. Each market participant may enter one or more bundles. A market participant with more than one entered bundle may specify substantiability among the entered bundles by entering one or more portfolio constraints into the data processing system. Acquisition trades may be distinguished from disposition trades using a signature represented by an algebraic sign of each of the proportions of the respective assets within the bundle. For example, assets to be acquired, hereinafter referred to as acquisition assets, may be represented by a proportion having a positive algebraic sign, and assets of which the market participant seeks to dispose, hereinafter referred to as disposition assets, may be represented by a negative algebraic sign. 
   As bundles are entered, the data processing system matches trades among the plurality of all bundles. The data processing system accomplishes the matching by assigning a set of non-negative numerical values to each bundle of the plurality of bundles entered which are to be incorporated into the match trade. Each of these numerical values represents the proportion by which each participating bundle is represented in the matched trade. That is, the numerical value represents the allocation of any particular participating bundle to the match trade. Then, the proportion of each asset in a particular bundle that is committed to the exchange is represented by the proportion of the asset in the bundle multiplied by the allocation value assigned by the data processing system to that particular bundle. 
   In one embodiment of the present invention, a trade is matched when the market surplus for each asset to be exchanged is non-negative. The allocation values are chosen by the data processing system so that this matching condition is satisfied. A non-negative market surplus in an asset occurs when the net valuation of the asset among disposing market participants is equal to, or exceeded by, the net valuation placed on the asset by acquiring market participants. The valuations, in turn, are represented by the proportions of each asset in each of the bundles forming the trade. 
   The data processing system implementing the bundle trading market may be a distributed data processing system. 
   The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter which form the subject of the claims of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  schematically illustrates bundled trades according to an embodiment of the present invention; 
       FIG. 2  illustrates a flow diagram of a method of bundled trading in accordance with an embodiment of the present invention; 
       FIG. 3  illustrates a flow diagram of a method of bundled trading in accordance with another embodiment of the present invention; 
       FIG. 4  illustrates a flow diagram of a method of market surplus redistribution in accordance with an embodiment of the present invention; 
       FIG. 5  schematically illustrates a matched transaction in accordance with an embodiment of the present invention; 
       FIG. 6A  schematically illustrates a matched transaction in accordance with an alternative embodiment of the present invention; 
       FIG. 6B  schematically illustrates a matched transaction in accordance with another alternative embodiment of the present invention; 
       FIG. 7  schematically illustrates an embodiment of a data processing system according to the present invention; 
       FIG. 8  illustrates, in block diagram form, a data processing system implemented in accordance with an embodiment of the present invention; 
       FIG. 9  illustrates flow diagrams of distributed data processing threads according to an embodiment of the present invention; 
       FIG. 10  illustrates a flow diagram of a method of trade matching in accordance with an embodiment of the present invention; 
       FIG. 11A  schematically illustrates the interaction of distributed data processing threads according to an embodiment of the present invention; 
       FIG. 11B  schematically illustrates the interaction of distributed data processing threads according to an alternative embodiment of the present invention; 
       FIG. 11C  schematically illustrates the interaction of distributed data processing threads according to another alternative embodiment of the present invention; 
       FIG. 12  illustrates, in block diagram form, a data processing system in accordance with an embodiment of the present invention; and 
       FIG. 13  illustrates a flow diagram of a method of allocation distribution according to an embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
   In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be obvious to those skilled in the art that the present invention may be practiced without such specific details. Refer now to the drawings wherein depicted elements are not necessarily shown to scale and wherein like or similar elements are designated by the same reference numeral through the several views. 
   An invention that addresses the problem of market fragmentation will now be described in detail. Refer now to  FIG. 1  in which a bundled trade is schematically illustrated. Bundled trade  100  includes four bundles, bundle  100   a , bundle  100   b , bundle  100   c  and bundle  100   d . Each of bundles  100   a - 100   d  may be associated with an individual market participant, but such an association is not essential. A particular market trader might, in principle, offer an unlimited number of different bundles for trade. Entries  101 - 104  in each of bundles  100   a - 100   d  are associated with an asset to be exchanged. Each entry  101 ,  102 ,  103 , and  104  is associated with an individual asset, assets  1 - 4 , in the embodiment of FIG.  1 . As described hereinabove, assets may incorporate anything of value. Furthermore, it is understood that bundles  100   a - 100   d  including only four assets to be exchanged are illustrative only, and that in practice, trade bundles would include a plurality of assets to be exchanged in which the plurality in a representative embodiment of the present invention could include more or less than four assets. 
   Trade bundles specify the proportion of each asset to be exchanged. The proportions of assets to be traded are represented by the figures within entries  101 - 104 . For example, the asset represented by entry  101 , asset  4 , in bundle  100   a  is to be exchanged in 1.5 units of that asset. This value and all the values in entries  101 - 104  are proportional values. That is, they represent the proportion of each asset to be exchanged in a particular bundle relative to a size of the bundle. The bundle size is represented in entry  105  in each of bundles  100   a - 100   d . Furthermore, the algebraic sign of each of the entry values is a signature that denotes whether the particular asset represented by the entry is an offer to acquire or an offer to dispose. In the embodiment of the invention illustrated in  FIG. 1 , acquisition offers are represented by entries having a positive algebraic sign and entries representing an offer to dispose have a negative algebraic sign. 
   It should be noted that an embodiment of the present invention may include assets none of which are money or currency. That is, an embodiment of bundle trading may exchange assets in which all exchanges are barter trades. Therefore, transactions in which in the context of a money exchange would otherwise be referred to as a buy and a sell are herein more generally referred to as an acquisition and a disposition, respectively. Moreover, it should be appreciated that the sign conventions in the embodiment of  FIG. 1  signalling acquisition offers and disposition offers may be arbitrarily selected, and the opposite sign convention may be employed in an alternative embodiment of the present invention. This will subsequently be discussed further when the methods of the present invention are described in detail. 
   The plurality of the portion values in each of bundles  100   a - 100   d  effectively represent limit “prices.” This is perhaps most easily seen if one of the assets in a bundle represents a currency. For example, if asset  1 , entry  101 , in bundled trades  100  represents a currency, then the market participant associated with bundle  100   d  is willing to pay, that is dispose, of one unit of currency in order to acquire a unit of asset represented by entry  102 , asset  2 . Note that this market participant would also be willing to give up one unit of asset  4 , represented by entry  104 , as well. Thus, from the perspective of the market participant associated with bundle  100   d , the transaction proposed is a combination of a barter transaction and cash transaction. Recall, however, that an embodiment of the present invention may include bundled trades in which no asset represents a currency. That is, an embodiment of the present invention, as discussed hereinabove, may include only barter trades. It is not necessary that at least one asset be a currency, although alternative embodiments of the present invention may include trade bundles having at least one asset which is a currency, and other alternative embodiments might include a plurality of assets representing different currencies. Because an embodiment of the present invention may include trade bundles that are purely barter transactions, it is more precise to regard the plurality of proportion values in each of bundles  100   a - 100   d  as relative valuations, rather than a “price.” 
   The data processing system of the present invention receives the bundled trades and selects bundles from among a plurality of bundles for participation in a particular transaction. Refer now to  FIG. 2  in which is schematically illustrated a flowchart of a method in accordance with the present invention. A bundled trade, including each of bundles  100   a - 100   d  of  FIG. 1 , is entered into a data processing system (see  FIGS. 8 and 12 ) in step  201 . In an embodiment of the data processing system of the present invention, the data processing system may be a distributed data processing system in which market participants enter trade bundles via a network, such as the Internet, through the intermediation of a data processing server. Such an embodiment will be subsequently discussed in greater detail. The data processing system then matches trades from among a plurality of entered trade bundles. The matching process encompasses steps  202 - 205  in FIG.  2 . 
   In matching the trade, each bundle that is participating in a particular trade is assigned a relative allocation by the data processing system. In step  202 , an allocation value is assigned to each of the bundles included in the match trade from among the plurality of entered bundles. For the purposes of further description of the present invention, it is convenient to introduce the indexed variable, x j , to represent the set of allocation values. The index “j” represents the bundle number of bundles in the matched trade. The proportions of each asset in the plurality of assets in each of the bundles are then weighted by the respective allocation value for each of the trade bundles in step  203 . It is convenient for the purpose of further discussion to introduce the doubly indexed quantity z ij  to represent the plurality of all asset proportions for all of the asset entries in all of the bundles in the bundle trade. As above, “j” represents the bundle number, and “i” represents the asset associated with the asset proportion “z ij ”. The maximum value that i can assume is the number of assets that may be traded in an embodiment of the present invention, and, as hereinabove noted, the maximum value of j is given by the number of bundles included in the match trade. In this notation, the step of weighing the asset proportions by the allocation values in  203  may be represented as:
 
 y   ij   =x   j   z   ij   ∀i ε{1 , . . . ,m}, j ε{1 , . . . ,n}   (1)
 
   The weighted asset proportions have been symbolized by the further notation “y ij ”. The maximum number of assets that may be traded in an embodiment of the present invention is represented by the symbol “m”, and the number of trade bundles in the match trade has been denoted by the symbol “n”. A market surplus is then calculated for each asset in step  204 . The market surplus for each asset will be denoted by the symbol “μ i ”. In an embodiment of the present invention, the market surplus for each asset according to step  204  is given by: 
   In step  205 , if the market surplus for each asset is non-negative, then the data processing system will redistribute the market surplus in step  207 . The step 
               μ   i     =     -       ∑     j   =   1     n     ⁢           ⁢       y   ij     ⁢     ∀     ⅈ   ∈     {     1   ,   …   ⁢           ,   m     }                       (   2   )             
 
of redistribution, step  207 , will subsequently be further described in detail. If the market surplus for each asset is not non-negative, then the trade match based on the assigned set of allocation values is not a successful match, step  206 . The data processing system must then search for another trade match among the plurality of entered trade bundles. In an embodiment of the present invention according to step  205 , acquisition offers have a positive algebraic sign and disposition offers have a negative algebraic sign. In an alternative embodiment in which the opposite sign invention is adopted, the condition with respect to the market surplus in a step corresponding to step  205  is that the market surplus be non-positive.
 
   In the event a trade match is unsuccessful, the data processing system might search among the entered bundle trades using a trial and error process. However, in the data processing system in which the number of entered trade bundles is realistic, such a method is likely to be inefficient and slow. Therefore, a systematic process for finding match trades is to be preferred. 
   An embodiment of the present invention implementing a systematic process for matching trades will now be described. Refer now to  FIG. 3  in which a flow diagram of a method for matching trades by an optimization process is illustrated. In step  300 , a constraint set is defined. In an embodiment of the present invention wherein trade matching is accomplished by an optimization process, a member of the constraint set is the requirement that the market surplus for each asset be non-negative, as described hereinabove. In terms of the symbol μ i , the first member of the constraint set becomes μ i ≧0, in an embodiment in which acquisition assets are represented by positive algebraic sign and disposition assets by negative algebraic sign. In an alternative embodiment having an opposite sign convention, the first member of the constraint set becomes μ i ≦0. The second member of the constraint set imposes a constraint on the allocation values which are to be determined as a solution to the optimization process. In an embodiment of the present invention, the second member of the constraint set may be:
 
0 ≦x   j   ≦u   j   ∀j ε{1 , . . . ,n}.   (3)
 
The symbol “u j ” has been introduced for convenience and denotes the bundle size, discussed previously, of bundle number “j”. In an alternative embodiment of the present invention, the second member of the constraint set may be taken to be:
 
             ∑     j   =   1     n     ⁢           ⁢     x   j       ≤   1     ,       
 
and
 
 x   j ≧0 ∀j ε{1 , . . . ,n}.   (4
 
In step  301 , an objective function is defined. In an embodiment of the present invention, an objective function may be a so-called convex combination of the market surpluses of each of the assets, that is, the μ i . It is convenient to introduce the following notation for this convex combination of market surpluses: 
                 ∑     i   =   1     m     ⁢           ⁢       c   i     ⁢     μ   i         ,       c   i     ⁢           ⁢     real   .               (   5   )             
 
   In this expression, the “c i ” are preselected constants representing the weighted contribution that asset “i” makes to the objective function. A preselected set of the c i  defines a particular embodiment of a bundled trade data processing system of the present invention. Alternative selections define alternative embodiments. Market participants may elect to enter trades into one or another of competing embodiments depending on the preselected set of c i . This will subsequently be illustrated by way of example. 
   The set of allocation values, x j , are determined by a step of extremization of the objective function in step  302 . The step of extremization, step  302 , may be either a maximization or a minimization, depending on the sign convention adopted for the set of asset proportions, z ij , previously discussed. Thus, in an embodiment of the present invention wherein a positive value for a z ij  is a signature for an acquisition trade and a negative value for a z ij  is a signature of a disposition trade, then the step of extremization, step  302 , is a maximization step. Conversely, in an embodiment having a sign convention wherein a negative value of z ij  is a signature of an acquisition transition and a positive value of a z ij  is a signature for a disposition trade, then the step of extremization, step  302 , is a minimization step. The extremization step, step  302 , determines the set of allocation values, x j , outputted in step  303 . Note that because the extremization is subject to the constraint set, and the first member of the constraint set requires that the market surplus for each asset be non-negative, step  205  of  FIG. 2  is necessarily satisfied, and a satisfactory trade match is obtained. 
   After the set of allocation values are outputted, it is necessary to distribute an allocation in step  304 , among the matched trade bundles such that the bundle having the smallest bundle size, u j , in proportion to its allocation value, x j , is just exhausted by the matched trade. This can be accomplished by rescaling the allocation values, x j , according to the following, detailed in steps  1300 - 1302  of FIG.  13 :
 
 v   j   =αx   j   ∀j ε{1 , . . . ,n}, 
 
where α≡min u   j   /x   j .  (6)
 
The symbol “v j ” represents the actual transaction allocation for bundle number “j”. Transaction asset allocations are then determined by multiplying the asset proportions z ij  by the actual transactions allocations v j , in step  1303 .
 
   The optimization process also yields the imputed prices of the assets exchanged in step  305 . These are the so-called duals known in the linear programming art. The duals represent the marginal change in the objective function due to a marginal change in the constraints. In an embodiment of the present invention, the constraint set includes the asset proportions. Thus, a subset of the duals represents the marginal change in the asset proportions required to produce a marginal increase in the objective function, Equation (5). That is, those duals represent the “cost,” or “price,” in unit asset terms, of marginally increasing the aggregated market surplus represented by the convex combination in Equation (5). The asset “prices” are measured in terms of that combination, and are termed the imputed prices of the respective asset. For example, an embodiment of the present invention might include as assets each of the European currencies that will be combined to form the Euro. Preselecting the c i  in Equation (5) to match that combination, would then yield market surplus in Euros, and the imputed price of each asset would be measured in Euros. Imputed prices will subsequently be illustrated by way of example. In step  305 , imputed prices for each asset are outputted, and the imputed price for the bundle, calculated by adding up the imputed asset prices weighted by each asset&#39;s proportion in the bundle, are outputted in step  306 . It then remains to redistribute the market surplus, as in step  207  of  FIG. 2 , which will now be discussed in detail. 
   Refer now to  FIG. 4  illustrating a flowchart detailing the market surplus redistribution in step  207  in FIG.  2 . In step  400 , sets of redistribution values are selected. The set of redistribution values includes a value associated with each asset and each bundle for a total of m×n such values. In addition, the set of redistribution values includes an additional “m” values, one for each asset, that is associated with a market participant in the role of “market maker.” In an embodiment of the present invention, the data processing system itself may play the role of the market maker. Thus, the set of redistribution values includes m×(n+1) values in total. Moreover, each redistribution value must lie in the range of values from zero to one, inclusive, and the subset of redistribution values associated with asset number “i” must add up to one when summed over all match trades plus the redistribution value associated with the market maker for asset number “i”. It is convenient to introduce the notation “W ij ,” to denote the set of redistribution values. In terms of this notation, the properties of the redistribution values heretofore recited may be written as follows:
 
 W   ij′   ,i ε{1 , . . . ,m}, j ε{0}∪{1 , . . . ,n} 
 
0 ≦W   ij ≦1 ∀i, j ′ and  (7)
 
                 ∑       j   ′     =   0     n     ⁢           ⁢     W   ij       =     1   ⁢     ∀     ⅈ   .                 (   7   )             
 
   In step  401 , the market surplus is apportioned by forming the m×n values in accordance with: W ij μ i α, iε{1, . . . ,m}, jε{1, . . . ,n}. In similar fashion, the market maker&#39;s share is allocated in step  402  in accordance with: W i0 μ i α, iε{1, . . . ,m}. An embodiment having no redistribution would simply have all of the “W ij ” equal to zero, and “W i0 ” equal one. 
   In an embodiment of the present invention, the market maker may retain this allocation as a fee. A special case of such an embodiment is an embodiment in which one or more of the assets to be traded is a currency, and the market maker retains an allocation in that asset in accordance with step  402 . That allocation may be interpreted as a commission. Such an embodiment will be subsequently discussed by way of example. 
   Transaction volumes are allocated among the matched bundled trades in step  403 . In this step, the actual amounts of each asset to be exchanged among the market participants are allocated in accordance with:
 
 z   ij   v   j   +W   ij μ i   αi ε{1 , . . . ,m}, j ε{1 , . . . ,n }.   (8)
 
   There are two important points with respect to the step of redistribution of the market surplus. From the properties of the asset proportions “z ij ” and the redistribution values, “W ij ”, as well as the market surpluses “μ i ”, as discussed hereinabove, each market participant is in a better position with respect to each asset in the bundle than it otherwise would have been in the absence of the redistribution. In other words, a market participant in a dispositional transaction with respect to asset number “i” disposes of less of that asset than it otherwise would have in the absence of redistribution, and a market participant in an acquisitional transition receives a greater amount of that asset than he otherwise would have received in the absence of redistribution. The other point is that the preselected values in an embodiment of the present invention for the W ij , effectively define the structure of the bundled trading market data processing system for that embodiment. Therefore, an electronic market place that is an embodiment of the present invention having a first preselected set of values W ij , may compete with an alternative embodiment of an electronic bundled trading market having a second preselected set of values W ij . Market participants may select among competing embodiments in accordance with a redistribution defined by the alternative preselected sets of redistribution values. Before discussing an electronic market place embodied in a distributed data processing system of the present invention, two embodiments of the present invention including the step of redistribution,  207 , will be described by way of example with respect to bundled trade  100 . 
   Refer now to  FIG. 5  in which a bundled trade transaction  500  is illustrated in tabular form. In transaction  500 , trade bundles  100   a - 100   d  have been matched with the allocation values as shown in fields  501   a - 501   d , respectively. The market surplus associated with each of the assets represented in fields  101 - 104 , assets  1 - 4 , are shown in fields  502 - 505 . As the values appearing in fields  502 - 505  show, the market surplus for each of the assets represented is non-negative. Thus, transaction  500  represents the successful match with respect to bundles  100   a - 100   d , in accordance with the previous discussion. In fields  506   a - 506   d  are shown the redistribution values corresponding to trade bundles  100   a - 100   d  for the asset represented in field  101 , asset  1 . Similarly, fields  507   a - 507   d  represent the redistribution values for the second asset in the transaction, the asset represented in the trade bundles by field  102 , asset  2 . Likewise, fields  508   a - 508   d  and fields  509   a - 509   d  represent the redistribution value for the third and fourth assets, those represented by fields  103  and  104  in bundles  100   a - 100   d , to be exchanged in transaction  500 . 
   In an embodiment of the bundled trading system of the present invention represented in transaction  500 , each trade bundle  100   a - 100   d , participates equally in the redistribution of the market surplus. This is apparent in that with respect to each asset, the redistribution value for each bundle is the same. However, it should be noted that this is not essential, and a different embodiment may have redistribution values such that different market participants, as represented by their bundled trades, receive different redistributions of the market surplus with respect to any or all of the assets in the trade bundle. 
   In transaction  500 , the market maker also participates in the redistribution of the market surplus. Fields  506   e - 509   e  contain the redistribution values for each asset in the transaction that determine the market maker&#39;s share of the market surplus with respect to each of the assets. Thus, in field  506   e , the market maker receives a ten percent share with respect to the market surplus in asset  1 , corresponding to field  101 . Similarly, as shown by the values in fields  507   e - 509   e , respectively, the market maker receives a twenty percent share of the market surplus with respect to asset  2 , a ten percent share of the market surplus with respect to asset  3 , and a forty percent share of the market surplus with respect to asset  4 , the assets corresponding to fields  102 - 104 . The market maker&#39;s share of the market surplus may be viewed as the market maker&#39;s “fee” or “commission.” However, as discussed hereinabove, transaction  500  may be a barter transaction, in which none of the assets traded represent money. 
   The actual amount of assets to be exchanged among market participants, a so-called transaction volume, is then found according to Equation (8). The transaction volume for each bundle with respect to the first asset is given in fields  510   a - 510   d . In transaction  500 , negative transaction volumes correspond to assets that are being disposed of in a given bundle, and transaction volumes with a positive value are assets being acquired in a given bundle. Fields  511   a - 511   d ,  512   a - 512   d , and  513   a - 513   d  are the transaction volumes for each bundle for assets  2 ,  3 , and  4 , respectively. The market maker&#39;s share of each asset appears in field  510   e - 512   e . Several points with respect to the transaction volumes will now be discussed. 
   Transaction  500  exhausts the supply of asset  3  in bundle  100   a . The market participant with respect to bundle  100   a  has entered a bundle trade in which it seeks to dispose of 30 units of asset of the third asset, represented by field  104 . Field  104  in bundle  100   a  contains the asset proportion value of −1, and the bundle size of bundle  100   a  is 30 units, as shown in field  105  in bundle  100   a . In exchange, the market participant with respect to bundle  100   a  acquires 47.57 units of the first asset in the bundle, represented by field  101 . Note that market participant with respect to bundle  100   a  sought 45 units of the first asset in the bundle, in accordance with the asset proportion value of 1.5 in field  101  of bundle  100   a , and a bundle size of 30 in field  105  of bundle  100   a . Thus, by virtue of the redistribution, the market participant with respect to bundle  100   a  has obtained slightly more of the first asset than it sought. In addition to the 30 units of the third asset, represented by field  104 , the market participant with respect to bundle  100   a  also had to give up 28.7 units, field  510   a , of asset  4 , represented by field  104  in bundle trade  100   a . The market participant with respect to bundle  100   a  had offered up to 30 units of asset  4 , in accordance with an asset proportion value of −1 in field  104 , in bundle  100   a , and a bundle size of 30 units, field  105  of bundle  100   a . Thus, the market participant with respect to bundle  100   a  has had to “pay” slightly less in asset  4  than his limit order with respect to that asset, by virtue of the redistribution of the market surplus. 
   The market maker has received 1.14 units of the first asset, represented by field  101 , the value in field  510   e . The market maker&#39;s allocation is in accordance with Equation (7). The market maker receives no allocation with respect to the second and third assets because, as seen in fields  503  and  504 , as there was no market surplus with respect to those assets. With respect to asset  4 , the market maker received 3.6 units, as seen in field  513   e.    
   Refer now to  FIG. 6  in which transaction  600  in accordance with another embodiment of the present invention is depicted. In transaction  600 , allocation values  601   a - 601   d  corresponding to bundles  100   a - 100   d , respectively, are determined in accordance with an embodiment of the present invention using an optimization step, such as step  302  of FIG.  3 . In this embodiment, the market surplus with respect to asset  4  has been used as the objective function. That is, in terms of Equation (5), the c i  corresponding to assets  1 - 3 , c 1 , c 2 , and c 3 , are all zero and c 4  has a value of 1. The market surplus with respect to three of the four assets included in bundles  100   a - 100   d , corresponding to asset proportions represented in fields  101 - 103 , respectively, are zero, as shown in fields  602 - 604 . For illustrative purposes, asset  4 , corresponding to asset proportions included in field  104 , may be considered a currency. The market surplus with respect to the currency is shown in field  605  to be 0.29 units of the currency. 
   In the embodiment of the present invention in transaction  600 , the redistribution values associated with each of the noncurrency assets are preselected to be zero with respect to each trade bundle  100   a - 100   d . This is shown in fields  606   a - 606 d,  607   a - 607   d , and  608   a - 608   d . Concomitantly, the redistribution value associated with the noncurrency assets with respect to the market maker is, therefore, 1, as shown in fields  606   e ,  607   e , and  608   e . That is, in the embodiment of transaction  600 , the market maker plays the role of a market specialist in a traditional exchange with respect to the noncurrency assets. In such an embodiment, the market maker retains his share of the noncurrency assets as an inventory which he may then dispose of as a market participant. 
   The currency is redistributed according to redistribution values in fields  209   a - 609   e . With respect to the currency, the market maker receives a ten percent allocation of the market surplus,  609   e . With respect to the market participants corresponding to bundles  100   a - 100   d , the market surplus in the currency is allocated according to redistribution values preselected in proportion to the respective allocation values for each bundle,  601   a - 601   d . These redistribution values are shown in fields  609   a - 609   d , respectively. This simply says that in the market embodiment of transaction  600 , each market participant receives payment, or makes payment, as appropriate, in proportion to the amount of its bundle that is exchanged. 
   Transaction  600  exhausts bundle  100   a  with respect to the third asset, in accordance with the asset proportion, field  104 , of bundle  100   a  and a bundle size, field  105 , of bundle  100   a . This is in accordance with Equation (6), which ensures that at least one bundle included in a matched trade will be exhausted. Market participant with respect to bundle  100   a  acquires 45 units of the first asset, in accordance with the asset proportion in field  101  of bundle  100   a  and the bundle size in field  105  of bundle  100   a . However, the market participant also has to pay 22.29 units of currency, field  613   a , in order to secure the 45 units of the first asset in exchange for its 30 units of the third asset. Nevertheless, due to the redistribution of the market surplus, the market trader with respect to bundle  100   a  pays less than his limit price of 30 units corresponding to the asset proportion value of −1 for the currency asset, field  104  in bundle  100   a , and the bundle size of 30 units in field  105  of bundle  100   a.    
   The assets acquired in bundle  100   a  are supplied by dispositions in the remaining bundles, bundles  100   b - 100   d . Thus, the 45 units of the first asset in bundle  100   a , field  610   a , are supplied by a disposition of 32.14 units in bundle  100   b , field  610   b , and a disposition of 12.9 units from bundle  100   d , field  610   d . Likewise, the 30 units of asset  3  disposed of by the market participant in bundle  100   a  are acquired as 10.71 units in bundle  100   b , field  612   b , and 19.29 units in bundle  100   c , field  612   c . This is a consequence of there being no market surplus with any asset other than the currency, and therefore, there is nothing for the market maker to inventory. 
   In transaction  600 , the optimization step, for example step  302  in  FIG. 3 , yields imputed prices for assets  1 ,  2 , and  3 , as discussed hereinabove. These =imputed prices are displayed in fields  614 ,  615 , and  616 , respectively. Because the optimization step in transaction  600  maximizes the market surplus in asset  4 , which for illustration has been interpreted to be a currency, the imputed prices in a fields  614 - 616  are measured in units of that market surplus, namely, currency units, as discussed hereinabove. In other words, the imputed price of a unit of asset  1  is 0.7143 units of the currency representing asset  4 , as shown in field  614 . Similarly, the imputed price of asset  2  is 1.43 currency units, field  615  and of asset  3 , 0.357 units of currency, field  616 . 
   Consider now bundle  100   a  in which 45 units of asset  1 , field  610   a , were exchanged for 30 units of asset  3 , field  612   a , and 22.29 units of currency, field  613   a . Multiplying the imputed price of asset  1  by 45 units and subtracting 30 times the imputed price of asset  3  yields a net price that the market participant with respect to bundle  100   a  must pay of 21.42 currency units. However, this price does not include the market participant&#39;s share of the market maker&#39;s commission. The market participant corresponding to bundle  100   a  enjoys share of the redistribution is proportionately larger, at 45 percent, field  609   a , than the redistribution received by the market participants. Thus, the market participant with respect to bundle  100   a  is responsible for a larger fraction of the market maker&#39;s commission. The market participant with respect to bundle  100   a  is, in fact, responsible for 50 percent of the market maker&#39;s commission because its 45 percent redistribution represents 50 percent of the aggregate redistribution to all the market participants. That is, the 45 percent in field  609   a  represents 50 percent of the redistribution net of the market maker&#39;s share. As previously described, the market maker&#39;s share is 1.71 units of currency,  613   e . Thus, the market participant with respect to bundle  100   a  is responsible for 50 percent of that, or 0.86 units of currency. Adding this to the net price it must pay with respect to the assets, yields the 22.29 units of currency that the market participant with respect to bundle  100   a  must pay, as previously discussed, and displayed in field  613   a . The transactions with respect to bundles  100   b - 100   d  can be interpreted in similar fashion. 
   Although the embodiment of the present invention represented in transaction  600  is convenient in order to describe the intuitive interpretation hereinabove recited, such interpretation is unnecessary to the implementation of the present invention. 
   In yet another embodiment of a bundled trading mechanism according to the principles of the present invention, traders may offer trade bundles in which bundles may serve as substitutes for each other. As discussed in conjunction with  FIG. 1 , each market participant may offer one or more trades. Any individual market participant may consider a preselected subset of its set of trades to be substitutable, one for another. In other words, with respect to a preselected subset of offered trades, a market participant might be indifferent as to exchanges with respect to any members of the subset. For example, if a first bundle and a second bundle were perfect substitutes, then the market participant offering to exchange those bundles would be indifferent as to whether a trade matched the first bundle or the second bundle. More generally, a market participant may not be completely indifferent as to exchanges of bundles, and weight the exchange of preselected bundles in the subset. An embodiment of the present invention which incorporates bundle substitution will now be described. 
   In an embodiment of the present invention, substitution of bundles entered by a market participant is effected when transaction volumes are allocated among the matched trades. Allocation of transaction volumes have been discussed hereinabove in conjunction with  FIG. 4. A  market participant indicates to the allocation mechanism, the substitutability of bundles by entering one or more portfolio constraints. For a particular market participant, a set of portfolio constraints may be defined by: 
                 ∑     j   ∈     T   k         ⁢           ⁢       a   kj     ⁢     x   j         ≤     b   k             (   9   )             
 
where j indexes the trade bundles, and k indexes the constraint. The x j  are the allocation values discussed hereinabove in conjunction with FIG.  2 . Recall that a market participant may specify more than one portfolio constraint. The bundle index, j, only runs over the trade bundles corresponding to the particular market participant, and T denotes the set of all bundled trade offers belonging to the particular market participant. The quantities a kj  are a set of portfolio weights supplied by the market participant to specify his or her bias with respect to the substitutability of bundle trade offers. For example, if a market participant were indifferent as between two bundles, then the weights assigned those two bundles in a portfolio constraint would be equal. The constraint limits b k  are specified by the market participant and ensure that no more than b k  units of bundles, substituted according to the kth portfolio constraint, are exchanged, in total.
 
   Alternatively, j may be taken to index trade bundles associated with the “kth” portfolio constraint, jεT k , where T k  is the set of bundles associated with the “kth” portfolio constraint. The sets T and T k  are either the same, or, at most, differ only with respect to members that correspond to portfolio weights having the value zero. Thus, the portfolio constraints are the same in either case. 
   In allocating trade volumes, the allocation mechanism must not allocate a trade volume that violates a market participant&#39;s portfolio constraint. Note that in this embodiment, portfolio constraints are imposed when trade volumes are allocated, not when bundles are matched. The portfolio constraints corresponding to a particular market participant involved in a matched trade are accounted for by first defining a quantity δ t  by: 
                 S   t     ≡     min   ⁢           ⁢       b   k         ∑     j   ∈   T       ⁢           ⁢       a   kj     ⁢     x   j               ,     k   ∈     C   T               (   10   )             
 
where t indexes the set τ, the set of all market participants involved in a particular matched trade, and C T  denotes the set of portfolio constraints corresponding to a particular market participant. Thus, δ t  represents the most restrictive portfolio constraint associated with the “tth” market participant in the particular matched trade. Then, the most restrictive of the portfolio constraints from among all of the market participants involved in a particular matched trade may be satisfied by defining: 
             β   ≡       min     t   ∈   i       ⁢     {     S   t     }               (   11   )             
 
and, forming actual transaction allocations v j  as in Eq. (3), but with α, in this embodiment, defined by:
 
 ∝≡min{β, min{ u   j   /x   j   }∀j ε[1 , . . . ,n].   (12)
 
The u j  are the bundle sizes previously discussed in conjunction with FIG.  3 . In this way, the actual allocation also ensures that bundles are not oversubscribed in the particular matched trade.
 
   After transaction volumes have been allocated, bundle sizes u j  and constraint limits b K  must be updated to account for the partial depletion of bundles because of the exchange. The updated values, u′ j  and b′ k  are respectively given by
 
 u′   j   =u   j   −v   j   , ∀jεT   k   (13)
 
and 
               b   k   ′     =       b   k     -       ∑     j   ∈   T       ⁢           ⁢       a   kj     ⁢     v   j                   (   14   )             
 
The portfolio constraints do not modify the market surpluses μ i , Eq. (2), or imputed prices. The allocation of trade volumes for bundle trade offers subject to portfolio constraints may be further understood by referring now to  FIG. 6B , in which an example of such a bundled trade is illustrated.
 
     FIG. 6B  illustrates bundled trade  600 B. Bundled trade  600 B differs from bundled trade  600 A in  FIG. 6A  only in that it is subject to a set of portfolio constraints, and in the addition of a fifth bundle, bundle  100   e . Bundles  100   a  and  100   b  are associated with a first market participant, labelled trader  1 , and bundles  100   c - 100   e  are associated with a second market participant, trader  2 . Because bundles  100   a - 100   d  are the same as bundled trade  600 A in  FIG. 6A , the matched exchange with respect to bundled trade  600 B is the same as that in bundled trade  600 A. Thus, the allocation values x j  are also the same for these bundles. Bundle  10   e  does not participate in the matched exchange. In other words, the allocation value, x j , corresponding to bundle  100   e  is equal to zero. The allocation values corresponding to bundles  100   a - 100   d  are the same as in bundled trade  600 A, and, for clarity, have not been shown in FIG.  600 B. Although, the matched exchange in bundled trade  600 A and  600 B are the same, the portfolio constraints in bundled trade  600 B give rise to a different transaction volume in bundled trade  600 B than the transaction volume in bundled trade  600 A. 
   In bundled trade  600 B, there is a single portfolio constraint associated with trader  1 , and two portfolio constraints associated with trader  2 . These are specified by assigning portfolio weights, a ki , and constraint limits, b k    
   The portfolio weights, a ki , corresponding to the portfolio constraint imposed by trader  1 , are shown in fields  620   a  and  620   b , to be equal to one for both bundle  100   a  and bundle  100   b . Thus, trader  1  is indifferent as to the substitution of bundles  100   a  and  100   b  in a matched trade, in this example. The constraint limit for this portfolio constraint has the value  30 , in field  623 . 
   With respect to trader  2 , there are two sets of portfolio weights and constraint limits. The portfolio weights for the first portfolio constraint imposed by trader  2  are shown in fields  621   c - 621   e , corresponding to bundles  100   c - 100   e . With respect to the first portfolio constraint of trader  2 , the weights are all equal to one. In a matched trade in which all three bundles,  100   c - 100   e  participate, trader  2  is indifferent as to substitution of these bundles, one for another. This portfolio constraint has a constraint limit of 85, in field  625 . 
   However, in a matched exchange in which only bundles  100   c  and  100 d participate, trader  2  is not indifferent as to the substitutability of these bundles. With respect to the second portfolio constraint of trader  2 , the portfolio weight attached to bundle  100   c  is equal to two, in field  622   c , and the portfolio weight of attached to bundle  100   d  is equal to one, in field  622   d . Thus one units of bundle  100   c  is substitutable for two unit of bundle  100   d . There is no substitution of bundle  100   e  in this portfolio constraint as indicated by its portfolio weight of zero, in field  622   e . The constraint limit for this portfolio constraint is 75, in field  627 . 
   The limiting portfolio constraint is the constraint associated with the first trader. The values of δ t  for each of the portfolio constraints appear in fields  624 ,  626  and  628 . The smallest value is 44.21, for the portfolio constraint imposed by the first trader. 
   The limiting portfolio constraint controls the allocation volumes. The value of the ratio u j /x j  for each of bundles  100   a - 100   d  is shown in fields  629   a - 629   d , respectively. (Because the allocation value, x j , for bundle  100   e  is zero, bundle  100   e  is not involved in the transaction, and no value has been entered in field  629   e .) The value of δ t  corresponding to the limiting portfolio constraint is smaller than any value of u j /x j . Thus, transaction amounts are determined by the smallest value of δ t  in accordance with Eq. (11). The transaction amounts for bundled trade  600 B are given in fields  610   a - 613   a  for each of the assets in bundle  100   a , and similarly with respect to fields  610   b - 613   b ,  610   c - 613   c , and  610   d - 613   d . Comparing these transaction amounts for bundled trade  600 B with the corresponding transaction amounts for bundled trade  600 A, in  FIG. 6A , it is seen that the transaction amounts with the portfolio constraint, bundled trade  600 B, are reduced by the ratio of 44.12:60 from the transaction amounts without the portfolio constraint, bundled trade  600 A, FIG.  6 A. Market surpluses and imputed prices are the same as in bundled trade  600 A,  FIG. 6A , and have been omitted from bundled trade  600 B for clarity. 
   In an alternative embodiment of the present invention including substitutability of bundles, portfolio constraints may be applied when trades are matched. In such an embodiment, the set of portfolio constraints Equation (9) are incorporated into the constraint set specified by Equation (3), in accordance with step  300  of FIG.  3 . Then in step  302  of  FIG. 3 , allocation values, xj, are determined as previously described in conjunction with FIG.  3 . Actual transaction allocations vj, in step  304 , are then determined according to Equation (6). 
   In yet another alternative embodiment of the present invention, the portfolio constraints, Equation (9) may be incorporated into the constraint set, in step  300  of  FIG. 3 , with the second member as specified in Equation (4). The set of allocation values, x j , is determined in step  302 , by a step of extremization of the objective function, which is defined in step  301 , and may remain in accordance with Equation (5). 
   A data processing system, such as data processing system  700  in  FIG. 7 , to be described, performs the method of the present invention by performing method steps such a those previously discussed, and in part made manifest in Equations (1)-(14). A specific embodiment of the present invention is instantiated through the choice of the preselected values appearing therein, and the process steps performed with respect thereto by the data processing system of the present invention. Calculational steps described in association with transaction  600  are for interpretive purposes only, in order to better understand the present invention. They do not necessarily represent literal process steps performed by the data processing system of the present invention, which will subsequently be described. 
   A distributed data processing system may provide the environment for asset bundle trading according to the method of the present invention. Refer now to  FIG. 7  in which is schematically illustrated such an embodiment of a distributed data processing system architecture, data processing system  700 . Data processing system  700  utilizes the World Wide Web to effect communication between market participants and the bundle trading market. 
   The “World Wide Web” (WWW) is a hypertext information and communication system used on the Internet with data communications operating according to a client/server model using a Hypertext Transfer Protocol (HTTP). HTTP is a known application protocol that provides users access to files using a standard page description language referred to as Hypertext Markup Language (HTML). It should be noted that HTML is an application of Standard Generalized Markup Language (SGML), an international standard (ISO 8879) for text information processing. Furthermore, the files that are accessed using HTML may be provided in different formats, such as text, graphics, images, sound, and video, among others. WWW functionality within data processing clients typically has been through the introduction of “web browsers” that allows for simple graphical user interface-based access to network servers. Two commercially available web browsers are Netscape Communicator™ and Internet Explorer™. Although the present invention as embodied in data processing system  700  employs the WWW for communication, such an embodiment is not essential to its practice. Alternative embodiments may employ other communication methodologies. 
   In data processing system  700 , a market participant communicates and interacts with the bundle trading market using its own data processing hardware, web client  701 . Web browser  702  incorporated in web client  701  provides the web services to web client  701 . Communications between the market participant and the bundled trading market are transported over the Internet  704 , the worldwide computer network. Web client  701  accesses the Internet  704 , through an internet service provider (ISP)  705  which web client  701  reaches via link  706 . Link  706  may be a telephone line to which web client  701  attaches by means of a data modem. Alternatively, link  706  might be a digital link such as Integrated Services Digital Networks (ISDN). In yet another alternative, web client  701  might attach directly to the Internet thereby eliminating link  706  and ISP  705 . 
   In data processing system  700 , bundle trading processor  707  is directly connected to the Internet  704  by means of its web server  708 . Communications between each market participant&#39;s web client, such as web client  701 , and the market is handled by web server  708 . Trade data is passed from web server  708  to bundle matching processor  709  in which trade execution takes place. Bundle matching processor  709  also passes trade data back to web server  708  for communication to web client  701  whence it becomes available to the market participant. Trade orders for execution are stored in a database, limit order table  710 , within bundle matching processor  709 . As trade orders are received, they are stored in limit order table  710 . Bundle matching processor then updates limit order table  710  as trades are executed. It also notifies traders about the execution via the Internet as previously described. These processes will be described in detail subsequently. Both order submission and transaction data processing are performed using distributed data processing. 
   Distributed processing in distributed data processing system  700  may be implemented using Java technology. Java is a programming language that is designed as a distributed and dynamic language. A Java capable web browser can download and execute Java applications, called applets, just as if the applet were an executable resident on the browser&#39;s host data processor. Web client  701  in data processing system  700  contains trade applet  711  in web browser  702 . The interactions of the market participant, using web client  701 , with the bundle trading processor  707  are through trade applet  711 . When a trader initially connects to bundle trading processor  707  over the Internet  704 , trade applet  711  is downloaded to web client  701 . Trade applet  711  receives and processes data sent by bundle trading processor  707 , as well as sending orders thereto. In performing these tasks, both trade applet  711  and bundle trading processor  707  may invoke Java methods that are implemented both on the server side, that is, on web server  708 , and the client side, that is, on web client  702  through trade applet  711 , respectively. 
     FIG. 8  illustrates a data processing system  800  that may be utilized to implement a web client  702  that executes the methodology of the present invention. Data processing system  800  comprises a central processing unit (CPU)  810 , such as a microprocessor. CPU  810  is coupled to various other components via system bus  812 . Read-only memory (ROM)  816  is coupled to the system bus  812  and includes a basic input/output system (BIOS) that controls certain basic functions of the data processing system  800 . Random access memory (RAM)  814 , I/O adapter  818 , and communications adapter  834  are also coupled to system bus  812 . I/O  818  may be a small computer system interface (SCSI) adapter that communicates with a disk storage device  820 . Communications adapter  834  interconnects bus  812  with an outside network enabling the data processing system to communicate with other such systems. Communications adapter  834  may be a modem in an embodiment of the present invention in which link  706  is a telephone line connecting web client  702  to ISP  705  by means of a dial-up connection. Alternatively, if link  706  is an ISDN line, communications adapter  834  might be an ISDN terminal adapter. Input/output devices are also connected to system bus  812  via user interface adapter  822  and display adapter  836 . Keyboard  824 , trackball  832 , and mouse  826  are all interconnected to bus  812  via user interface adapter  822 . Display monitor  838  is coupled to system bus  812  by display adapter  836 . In this manner, a user is capable of inputting to the system through keyboard  824 , trackball  832 , or mouse  826 , and receiving output from the system via speaker  828  and display  838 . Trade data transmitted to web client  701  by web server  708 , and processed for outputting by trade applet  711 , may be presented to the market participant on display  838 . 
   Similarly data processing system  800  may be utilized to implement bundle trading processor  707 . In such an embodiment, data processing system  800  may represent a high-end work station or minicomputer, and may include multiple processors,  810 . In a data processing system  800  implementing a bundle trading market, communications adapter  834  may be a network transceiver. 
   Some embodiments of the invention may include implementations as a computer system program to execute the method or methods described herein, and as a computer program product. According to the computer system implementation, sets of instructions for executing the method or methods are resident in RAM  814  of one or more computer systems configured generally as described above. Until required by the computer system, the set of instructions may be stored as a computer program product in another computer memory, for example, in disk drive  820  (which may include a removable memory such as an optical disk or floppy disk for eventual use in disk drive  820 ). 
   Moreover, as has been previously described, the computer program product can also be stored at another computer and transmitted in a computer readable medium when desired to the market participant&#39;s web client  701  by an external network such as the Internet  704 . One skilled in the art would appreciate that the physical storage of the sets of instructions physically changes the medium upon which it is stored so that the medium carries computer-readable information. The change may be electrical, magnetic, chemical, or some other physical change. While it is convenient to describe the invention in terms of instructions, symbols, characters, or the like, the reader should remember that all of these and similar terms should be associated with the appropriate physical elements. 
   Refer now to  FIG. 9  in which a flow chart illustrating an embodiment of a method of the present invention in a multithread computer environment is shown. Java is such a multithreading environment. Threads are computational units within a software program that carry out different tasks. Generally, threads are asynchronous. That is, one thread does not need to wait for another thread to complete execution before it can start running. 
   A bundled trade is entered when a market participant sends an order to bundle trading processor  707 . This is effected by trade applet  711  invoking a send order method which causes the launching of thread  900   a  in step  901 . Each time a market participant enters an order, another copy of thread  900   a  is launched. In step  902 , an order identification is generated. The order identification is a unique identifier that identifies each order in the market. The order identification is sent back to trade applet  711  in step  903 . A market participant may submit multiple orders and the order identification permits a trade applet, such as trade applet  711 , to associate, with the appropriate order, data pertaining to transactions with respect to each order entered. In step  904 , the order is added to an order database in limit order table  710 . If a market participant imposes one or more portfolio constraints, parameters specifying each constraint, as previously described, are entered into a portfolio constraint database in limit order table  710 . A portfolio identifier may be attached to each constraint by thread  900   a  to associate bundles in the limit order database with their corresponding portfolio constraints. The limit order database and portfolio constraint database will be discussed further below in conjunction with FIG.  11 . 
   Because a second market participant may enter an order before the thread entering an order from a first market participant has completed executing, it is possible that two orders may be assigned the same order identification. In an embodiment of the present invention, this can be prevented by forcing the send order method of thread  900   a  to be synchronous. That is, the thread launched by the second market participant&#39;s order entry cannot begin execution until the thread launched when the first market participant entered its order completes execution. 
   A market participant may also delete an order prior to its execution. When the market participant elects to cancel his order, trade applet  711  invokes a cancel order method, launching thread  900   b , in step  905 . In step  906 , the order identification of the order to be cancelled is added to a cancel order list in limit order table  710 . 
   A third thread  900   c  effects the execution of bundled trades. This thread launches in step  907  when a bundle trading “market”, such as bundled trading processor  707 , is initiated, and then continuously loops through the limit order database. First, in step  908 , orders in the order database are checked to see if they are in the cancel order list. If so, they are deleted from the database in step  909 , and the market participant is notified in step  910  through the invocation of methods implemented in the trade applet, such as trade applet  711 , as previously discussed. Then, in step  911 , trades are matched, and any portfolio constraints applied, using the methods of the present invention previously described hereinabove. Thread  900   c  retrieves any required portfolio constraint data from the portfolio constraint database. 
   In step  912 , the order identification of matched trades are compared with the current entries in the cancel order list. If a matched trade appears in the cancel order list, the order identification is deleted from the cancel order list, step  913 , and the market participant is notified, again through the trade applet, that his cancellation came too late. In any case, quantities are updated for matched trades, step  915 , and the market participants are notified, step  916 . As previously described, the trade applet receives the updated data and processes it for outputting to the market participant, for example by means of a graphic display of an order table on display  838 . 
   However, a market participant need not be associated with a human operator. An embodiment of the present invention may be utilized in a purely electronic marketplace in which trades are entered by an automated trading program. An illustrative example might be trading in shares of index funds. The fund&#39;s “trader”, a software program, seeks to buy or sell, as a bundle, all of the assets forming the index. Bundles are bought and sold as subscribers either acquire or dispose of shares of the fund. Buy orders and sell orders may be entered electronically via the Internet, for example, and the transaction between the subscriber and the fund closed by using electronic funds transfer. The trade data received via the trade applet might then be stored in RAM  814  or mass storage device  820  for further processing in closing the transaction. From the perspective of the bundle trading market, the market participants in this market are program trading data processing systems. 
   In  FIG. 10 , a flowchart is illustrated depicting the data processing of trade matching, step  911 , in further detail. In step  1000 , a hash table is generated that maps order identifications to bundle indices used in the matching algorithm as described hereinabove with respect to FIG.  2 . Step  1001  includes entering the order data contained in the order database into the matching optimization process previously described in conjunction with FIG.  3 . The optimization process outputs matched trade bundles identified by a bundle index. The hash table generated in step  1001  is used to identify matched orders in the order database by order identification, step  1002 . The transaction volumes and prices are then calculated using the method of the present invention previously described in association with  FIG. 4 , in step  1003 . In step  1004 , the order database is updated based on the transaction volumes. In other words, new u j  are calculated to account for the part of each bundle “j” exchanged in the transaction. This may be in accordance with Equation (13) in an embodiment of the present invention imposing portfolio constraints on the transaction volume allocation. If an order is fully matched, the new value of u j  for that bundle is zero, step  1005 . It then is deleted from the database in step  1006 . In an embodiment imposing portfolio constraints on the transaction volume allocation, the portfolio limits, b k , are also updated in step  1004 , and if the updated value is zero, in step  1005 , all bundles with non-zero weight in the corresponding portfolio constraint are deleted from the order database in step  1006 . Otherwise, it remains in the database, and may participate in further transactions. After the database is updated, the process continues in step  1007  with step  912 . 
   The operation of a data processing system according to an embodiment of the present invention may be further appreciated by referring to  FIG. 11A-11C . The operation of the asynchronous threads on the data structures within a data processing system according to the present invention, such as data processing system  700 , is schematically illustrated therein. 
   Referring to  FIG. 11A , a new trade bundle, bundle  1101 , is to be added to limit order database  1102 . Bundles within database  1102  are identified by order identifications, fields  1103   a - 1103   d , and  1103   v . The last order identification in database  1102  is “ 122 ” in field  1103   v . A first thread, corresponding to thread  900   a , generates the next order identification, “ 123 ” in field  1104 . It then adds the new order, bundle  1101  to database  1102 . 
   A market participant may cancel an order before it is executed. An order posted for cancellation, field  1106  containing the order&#39;s identification, here shown to be order “ 102 ”, is added to cancel order list  1107 , by a second asynchronous thread corresponding to thread  900   b.    
   The third thread in  FIG. 11A , corresponding to thread  900   c , is the trade matching thread. It monitors both database  1102  and cancel list  1107 . Orders within database  1102 , such as bundles  100   a - 100   d  shown, are continuously matched using the methods of the present invention heretofore described. If an order identification appears in cancel list  1107 , for example, order “ 105 ,” “ 112 ,” or “ 104 ,” in fields  1108 - 1110  respectively, it is deleted both from database  1102  and cancel list  1107  by thread  900   c . Matched trades in database  1102  are updated by thread  900   c  to reflect the exchange of assets resulting from the transaction. Thread  900   c  also notifies market participants via a trade applet, such as trade applet  711 . As previously discussed, notification is made with respect to both matched trades, cancelled orders, and if an order posted for cancellation had been executed before cancellation was attempted. 
   In an embodiment of the present invention in which market participants may specify portfolio constraints, as discussed hereinabove in conjunction with  FIG. 6B , the information processed by the threads must also include the information specifying the portfolio constraints. Referring to  FIG. 11B , there is illustrated therein an embodiment of limit order data base  1102  in which incorporates portfolio constraint data, as discussed hereinabove in conjunction with FIG.  6 B. The portfolio weights specifying constraints are stored in fields  1112 - 1119  in limit order data base  1102 . Each entry in fields  1112 - 1119  holds a pair of values, the first of which is the portfolio weight for the corresponding bundle in a portfolio constraint having an identifier corresponding to the second value in the pair. Portfolio identifiers are assigned when portfolio constraints are entered, via thread  900   a , for a given bundled trade, and are stored in portfolio constraint database  1120 . Portfolio constraint identifiers are stored in fields  1121 - 1123  in portfolio constraint database  1120 . Fields  1124 - 1126  in database  1120  include a market participant identifier. Thus, the first portfolio constraint identified as “1” is associated with trader  1 , field  1124 , and the remaining two portfolio constraints, identified as “2” and “3” are associated with trader  2 , fields  1125  and  1126 . It would be understood that other identifier symbols might be associated with portfolio constraints and market participants, provided they are unique. Portfolio constraint database  1120  effects the association between the two sets of identifiers. The entries in fields  1127 - 1129  in database  1120  represent the portfolio limits specified with each of the portfolio constraints. On execution of a matched trade by thread  900   c , thread  900   c  retrieves the portfolio constraint data from limit order data base  1102  when generating transaction volumes, as discussed in conjunction with FIG.  6 B. 
   Alternatively, all portfolio constraint data may be stored in a portfolio constraint data base. Such an embodiment is illustrated in  FIG. 11C  showing portfolio constraint data base  1130  therein. As bundle trades are entered, thread  900   a  adds the portfolio constraint data specified by the market participant to portfolio constraint data base  1120 . Fields  1131   a - 1131   c  in portfolio constraint data base  1120  include a trader identifier. Because trader  2 , as discussed in conjunction with  FIG. 6B , has specified two portfolio constraints, the identification of trader  2  appears twice, in fields  1131   b  and  1131   c , in portfolio constraint data base  1130 . A portfolio identifier appears in fields  1132   a - 1132   c . The identifier “1” in field  1132   b  identifies the respective portfolio constraint as the first portfolio constraint imposed by trader  2 . Similarly, the identifier “2” in field  1132   c  identifies the associated data as specifying the second portfolio constraint of trader  2 . The constraint limits for each of the portfolio constraints appears in fields  1133   a - 1133   c  in portfolio constraint data base  1130 . Fields  1134   a - 1134   c  contain an ordered pair of values, shown as enclosed in braces, the first value of which represents a trade bundle identifier from one of fields  1103   a - 1103   e  and  1103   v , in limit order data base  1102 , of the trade bundle to which the constraint applies, and the second value is the corresponding portfolio weight. Additional fields  1134  specify additional trade bundle identifiers corresponding to additional trade bundles to which the respective portfolio constraint applies, along with the corresponding portfolio weight. Thus, in fields  1134   d - 1134   h  are the trade bundle identifiers and portfolio constraint weights for each additional trade bundle to which each of the portfolio constraints applies. Because the first portfolio constraint of trader  2  applies to three trade bundles,  100   c - 100   e , a third identifier and portfolio weight pair corresponding to bundle  100   e , in  FIG. 6B , is included in field  1134   g . Note that portfolio constraint  2  of trader  2  applies to bundles  100   c  and  100   d  in FIG.  6 B. Bundle  100   e  corresponds to bundle identifier  104  in field  1103   e , and in field  1134   h , a weight of zero has been associated with bundle identifier  104 . Alternatively, field  1134   h  may be empty, thereby signifying to thread  900   c  that the bundle associated with identifier  104  does not participate in the second portfolio constraint of trader number  2 . Thread  900   c  retrieves the portfolio constraint data values from portfolio constraint data base  1130 , and generates transaction volumes as described in conjunction with FIG.  6 B. 
   As previously noted, a data processing system for matching bundle trades in accordance with the present invention is adaptable for a multiprocessor environment. Refer now to  FIG. 12  in which an embodiment of a bundle matching processor  709  having multiple processors is illustrated. Bundle matching processor  709  includes three central processing units CPUs  1200   a - 1200   c . These are connected to a system memory  1201  via system bus  1202 . Each of CPUs  1200   a - 1200   c  may be dedicated to executing, independently and asynchronously, a bundle trading thread in accordance with a method of the present invention. For example, CPU  1200   a  may execute thread  900   a  for entering bundle trades, as discussed hereinabove. Similarly, CPU  1200   b  may execute thread  900   c  for matching trades, and CPU  1200   c  may execute thread  900   b  for deleting bundle trades. System memory  1201  may include limit order table  710 . Alternatively, one CPU, say CPU  1200   a , may be dedicated to executing two threads, for example, thread  900   a  for entering bundle trades, and thread  900   c  for deleting bundle trades. In such an embodiment, one of the other two CPUs, for example, CPU  1200   c , may execute thread  900   b  for matching bundle trades. The remaining CPU may incorporate web server  708 , or alternatively web server  708  might be embodied in CPU  1200   a . It would be understood by one of ordinary skill in the art that the alternative embodiments represented by the various presentations of the multiprocessor tasks are all embraced within the disclosed methods and apparatus of the present invention. In yet another alternative embodiment, CPUs  1200   a - 1200   c  may execute threads in synchronous fashion. 
   Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.