scheduling the production of several items with random demands in a single facility consider the problem of scheduling the production of several items in a single facility that can produce only one item at a time this problem occurs since it is often economic to produce several items in a single facility the objective is to reduce the long run average holding backorder and setup costs we assume that demands are random with constant expected rates we allow backorders and charge holding and backlogging costs at linear time weighted rates items are produced at continuous constant rates setup times and setup costs are item dependent constants these parameters however are independent of the order of setups a real time scheduling tool is developed in three steps first with demands replaced by their expectations we compute an optimal or near optimal target cyclic schedule next we study the problem of scheduling the facility after a single disruption perturbs the inventories the goal is to recover the target cyclic schedule at minimal excess over the average cost of the cyclic schedule we formulate this as a control problem and obtain a linear recovery policy that is optimal for a large configuration of disruptions finally we select safety stocks to minimize the long run average cost of following the target schedule with the recovery policy we show that optimal safety stocks are unique and have the property that in the long run the proportion of time that an item is in stock is the ratio of backorder to holding plus backorder cost we present an example that integrates the cyclic schedule the control policy and the safety stocks

determination of safety stocks for cyclic schedules with stochastic demands abstract this paper considers the problem of scheduling the production of multiple items each with random demand on a single facility we show how the variance in demand during lead time can be estimated and present a model for determination of safety stocks and order up to levels for a fixed cyclic sequence both with and without idle time for systems with idle time we present a control model to make the decision to produce next item in sequence or idle the facility the performance of the model is tested in a simulation study

the american put option valued analytically an analytic solution to the american put problem is derived herein the hedge ratio and other derivatives of the solution are presented the formula derived implies an exact duplicating portfolio for the american put consisting of discount bonds and stock sold short the formula is extended to consider put options on stocks paying cash dividends a polynomial expression is developed for evaluating these formulae values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated tabulated and compared with values derived by numerical integration and binomial approximation as with european options evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods finally applications of this american put solution are discussed

cyclical schedules vs dynamic sequencing replenishment dynamics and inventory efficiency abstract this paper addresses the efficiency of fixed sequence cyclical scheduling systems relative to that of dynamically sequenced order point methods of production control the criterion for comparison is the aggregate inventory required to achieve a target fill rate taking into account the alternative replenishment dynamics arising under the respective systems a simulation analysis demonstrates that cyclical scheduling may have smaller aggregate inventory requirement when the production process is highly utilized and when this utilization is due to demand for a small number of items having large setup times

welfare implications of the bankruptcy reform act of 1999 abstract in recent years personal bankruptcy has become an important issue to consumers creditors and legislators alike over 40 billion dollars of unsecured debt were discharged in 1998 by 1 44 million households these losses have led legislators to propose a variety of changes in bankruptcy law the most important and recent of which is the bankruptcy reform act of 1999 ba99 i develop a dynamic stochastic general equilibrium model of personal bankruptcy to investigate the trade off between the consumption smoothing role of bankruptcy and the interest rate and deadweight costs it imposes i find that stringent means tests would reduce filing rates only slightly and would have only modest welfare consequences on the other hand the elimination of bankruptcy altogether is found to have substantial benefits this result is robust to income shock persistence and to stringency in the application of means tests

the pricing of futures and options contracts on the value line index this paper considers the problems peculiar to the value line index because of its use of geometric averaging as regards the pricing of options and futures on that index the value line composite index vlci is an equally weighted geometric average index of nearly 1700 stocks the vlci futures market has existed since 1982 while the vlci options market was established in 1985 this paper provides valuation formulas and analyzes the economic properties of these contracts because of the geometric averaging in the vlci its contingent claims have special properties for example the futures price may fall short of the spot price and the value of a vlci call option may decline when the volatility of the index is increased vlci futures are shown to provide a direct means for duplicating an equally weighted portfolio of the underlying stocks the value line composite index vlci is an unweighted geometric average of stock prices expressed in index form the index on june 30 1961 was set at 100 and subsequent values are compared against it futures contracts on the vlci are traded on the kansas city board of trade kcbt they were the first stock index futures to be traded in the united states starting on february 24 1982 unlike commodity futures contracts no delivery ever takes place instead any open contracts on expiration day are settled in cash according to the actual vlci value 1 more recent market innovations are options on the vlci that have been traded on the philadelphia stock exchange pse since january

assessing bankruptcy reform in a model with temptation and equilibrium default abstract a life cycle model with equilibrium default in which agents with and without temptation coexist is constructed to evaluate the 2005 bankruptcy law reform the calibrated model indicates that the 2005 reform reduces bankruptcies as seen in the data and improves welfare as lower default premia allows better consumption smoothing a counterfactual reform of changing income garnishment rate is also investigated interesting contrasting welfare effects between two types of agents emerge agents with temptation prefer a lower garnishment rate as tighter borrowing constraint prevents them from over borrowing while those without prefer better consumption smoothing enabled by a higher garnishment rate

a comparison of futures and forward prices abstract this paper uses the pricing models of cox ingersoll and ross 1981 richard and sundaresan 1981 and french 1982 to examine the relation between futures and forward prices for copper and silver there are significant differences between these prices the average differences are generally consistent with the predictions of the futures and forward price models however these models are not helpful in describing intra sample variations in the futures forward price differences this failure is apparently caused by measurement errors in both the price differences and in the explanatory variables

an analytic approximation for the american put price black and scholes 1 derived the pricing equation for a european put when the stock price follows geometric brownian motion for this same case merton 5 derived the pricing equation for an american put with infinite time to maturity brennan and schwartz 2 rubinstein and cox 7 and parkinson 6 have developed numerical solutions for the price of an american put numerical solutions are expensive and do not provide much intuition naturally an analytic solution would be much preferred unfortunately pricing the american put requires solving a formidable and presumably intractable boundary value problem

procrastination and obedience in this lecture i shall focus on situations involving repeated decisions with time inconsistent behavior although each choice may be close to maximizing and therefore result in only small losses the cumulative effect of a series of repeated errors may be quite large thus in my examples decision makers are quite close to the intelligent well informed individuals usually assumed in economic analysis but cumulatively they make seriously wrong decisions that do not occur in standard textbook economics this lecture discusses and illustrates several pathological modes of individual and group behavior procrastination in decision making undue obedience to authority membership of seemingly normal individuals in deviant cult groups and escalation of commitment to courses of action that are clearly unwise in each case individuals choose a series of current actions without fully appreciating how those actions will affect future perceptions and behavior the standard assumption of rational forwardlooking utility maximizing is violated the nonindependence of errors in decision making in the series of decisions can be explained with the concept from cognitive psychology of undue salience or vividness for example present benefits and costs may have undue salience relative to future costs

explaining the early discounts on stock index futures the case for disequilibrium 1984 explaining the early discounts on stock index futures the case for disequilibrium financial analysts journal vol 40 no 4 pp 43 47 67

household borrowing after personal bankruptcy a large body of literature has examined factors leading to filing for personal bankruptcy but little is known about household borrowing after bankruptcy this paper augments the existing literature with a comprehensive analysis of postbankruptcy borrowing using data from the survey of consumer finances we find that filers generally have more limited access to unsecured credit but borrow more secured debt after bankruptcy than comparable households that have never filed for bankruptcy filers also pay higher interest rates on all types of debt in addition as more time passes after filing credit access and borrowing costs improve however filers remain more prone than comparable nonfilers to experience financial distress accumulate less wealth and use expensive credit sources like payday loans even more than 10 years after filing

taxes and the pricing of stock index futures stock index futures prices are generally below the level predicted by simple arbitrage models this paper suggests that the discrepancy between the actual and predicted prices is caused by taxes capital gains and losses are not taxed until they are realized as constantinides demonstrates in a recent paper this gives stockholders a valuable timing option if the stock price drops the investor can pass part of the loss on to the government by selling the stock on the other hand if the stock price rises the investor can postpone the tax by not realizing the gain since this option is not available to stock index futures traders the futures prices will be lower than standard no tax models predict on 24 february 1982 the kansas city board of trade began trading futures contracts on the value line average stock index during the next two months both the chicago mercantile exchange and the new york futures exchange also initiated trading in stock index futures although these contracts are actively traded their prices have puzzled both practitioners and academics the observed

on valuing american call options with the black scholes european formula empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the black scholes european formula such biases have been found related to the exercise price the time to maturity and the variance we argue here that the american option variant of the black scholes formula has the potential to explain the first two biases and may partly explain the third it can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods the expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings the black scholes european option pricing model tends to exhibit systematic empirical biases when used to value american call options the reported biases

lot sizes in a capacity constrained facility a simulation study of stationary stochastic demand abstract this paper considers the scheduling of several different items on a single machine in literature known as the economic lot scheduling problem elsp one of the characteristics of this problem is that the demand rate is deterministic and constant however in a practical situation demand usually varies in this paper we examine if a deterministic model can be used if demand is stationary stochastic a dynamic programming approach from bomberger manage sci 12 11 1966 778 and a heuristic method from segerstedt int j production econom 59 1 3 1999 469 are used to calculate lot sizes for four items the production of these items is simulated with different variations in demand rates our conclusion is that a deterministic model of this kind can be used in a practical situation where the demand rate is stationary stochastic but the models must be complemented by a decision rule which item to produce and when to produce it in our tests the heuristic method and the dynamic programming approach perform rather similarly with respect to costs and inventory levels but the dynamic programming approach results in more backorders when there is small variation in demand rates this study indicates that the model used for determination of lot sizes is of less importance than the decision rule used for identification of the item to produce and when to produce it

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

the saga of the first stock index futures contract benchmarks models and learning in the presence of imperfect or perturbed benchmarks pricing based on relative valuation or arbitrage can be affected adversely this study highlights persistent pricing irregularities in the kansas city value line kcvl stock index futures market this contract is especially interesting because the underlying benchmark underwent a midstream change in definition from a complex equally weighted geometric index to an equally weighted arithmetic index empirical analysis reveals that during a four year period the market displayed herd like behavior and priced the kcvl geometric contract using the simple but wrong cost of carry benchmark model a dramatic change occurs around the publication of the eytan harpaz 1986 model when the market turns efficient from the perspective of this new model the market appears to have succumbed initially to a bad information cascade primarily because arbitrage was difficult to understand and carry out under complex benchmarking the evidence provides empirical extension to the observational social learning paradigms of simon 1955 banerjee 1992 and bikhchandani hirshleifer and welch 1992 that lead to behavioral herding and information cascades

forward and futures prices evidence from the foreign exchange markets empirical studies of the treasury bill markets have revealed substantial differences between the futures price and the implied forward price these differences have been attributed to taxes transaction costs and the settling up procedure employed in the futures market this paper examines the forward and futures prices in foreign exchange in an attempt to distinguish between the competing explanations empirical studies of the treasury bill market have revealed differences between the futures price or rate and the implicit forward price derived from the term structure of interest rates 1 these differences have generally been attributed to market imperfections such as taxes and transaction costs see for example arak 1 capozza and cornell 2 and rendelman and carabini 6 recently however cox ingersoll and ross 3 henceforth cir derived a model in which forward and futures prices need not be equal even in perfect markets without taxes as long as interest rates are stochastic the significance of the cir effect may be hard to investigate using only data from the bill market because of the potentially complicating effects of taxes and transaction costs unique to this market by using data from the foreign exchange market we are able to eliminate the tax effect and reduce the impact of transaction costs the question we address is whether the discrepancies observed in the treasury bill market are also observed in the foreign exchange market if they are then we have evidence that the differences are due to a combination of the cir effect and the transaction costs common to both markets if they are not then either the magnitude of the cir effect is much less in the foreign exchange market or the treasury bill results are due to the unique tax treatment and transaction costs of that market this paper is organized as follows in section i the trading mechanics of the forward and futures markets in foreign exchange are discussed section ii reviews the explanations for the discrepancies between the forward and futures prices for treasury bills the institutional differences between the foreign exchange and bill markets are also summarized to show which of these explanations cannot apply to the foreign exchange market in section iii the data are decribed and the empirical results are presented the conclusions are summarized in the final section

economic order quantities in production from harris to economic lot scheduling problems abstract this article provides a short historical overview from harris and his economic order quantity eoq formula to the economic lot scheduling problem elsp the aim is to describe the development of the elsp field from the eoq formula to the advanced methods of today in a manner that suits master and graduate students the article shows the complexities difficulties and possibilities of scheduling and producing several different items in a single production facility with constrained capacity the items have different demand cost operation time and set up time set up time consumes capacity and makes the scheduling more complicated idle time makes the scheduling easier but is bad from a practical point of view since it creates unnecessary costs due to low utilisation of the facility a heuristic solution method is used on a small numerical example to illustrate different solution approaches the solution method creates a detailed schedule and estimates the correct set up and inventory holding cost even if the facility works close to its capacity

playing the turn of the year effect with index futures the turn of the year effect is a well documented stock market phenomenon in which low capitalization small stocks receive relatively higher returns than high capitalization big stocks on the last trading day of december and the first 8 trading days of january the difference in returns during this period is of the order of 10 strategies for buying and selling these small stocks may be profitable but may also incur large transaction costs that eliminate most or all of the projected gains in this paper we show a preferable way to invest in order to exploit this anomaly use a futures spread that is long in the small stocks and short in the big stocks the optimal investment which uses a modification of the capital growth criterion is large and has a substantial expected gain with minimal risk we have used this analysis successfully in managing investment accounts