nonlinear pricing to produce information we investigate the firm s dynamic nonlinear pricing problem when facing consumers whose tastes vary according to a scalar index we relax the standard assumption that the firm knows the distribution of this index in general the firm should determine its marginal price schedule as if it were myopic and produce information by lowering the price schedule bunching consumers at positive purchase levels should be avoided as a special case we also consider a market characterized by homogeneous consumers with a static but unknown demand curve we show that when there are repeat purchases the forward looking firm should tend towards penetration pricing otherwise its strategy should tend towards skimming we extend our insights to more general settings and discuss implications for pricing product lines

inventory and sales effort management under unobservable lost sales a retailer needs to make decisions regarding how much to order and how much sales effort to exert in an environment with uncertain demand one intrinsic complexity in a typical retail environment is caused by the fact that the retailer can obtain information about demand only based on sales as demand itself is unobservable taking a bayesian approach lariviere and porteus 1999 show that in such a setting a retailer should stock more to increase the probability of an exact demand observation in this article we extend their work by allowing the retailer to control both the stocking quantity and sales effort which can be used to affect demand we show that their insights with respect to information stalking carry over to this setting in addition our model allows gaining a better understanding of optimal sales effort strategies we find that demand management has a dual role in supporting information gathering while at the beginning of a product life cycle it is optimal to support learning effects by sharply reducing sales effort at later stages of the product life cycle an aggressive strategy of increased promotional activities can be used to harvest the information gathered in earlier periods

determinants of pension plan fees in spain pension plans and funds represent a substantial part of the welfare systems in both europe and spain one of the most important factors in the choice of a plan or fund is the performance it obtains in view of the influence that fees have on performance the objective of this study is to analyse the variables that determine the management and custodial fees of individual pension plans the spanish market for pension plans and funds sets legal caps on these fees and at the same time the majority of them are commercialized and managed by financial institutions which can in turn generate a conflict of interests in this article we estimate models with censured variables and our findings show how the average investment per plan the legal status and the size of the management company to which the plan belongs and the style of the plan are all relevant determinants of the management fee in turn the custodial fee is determined by the legal status of the custodial company the size the return and the type

confidence based optimisation for the newsvendor problem under binomial poisson and exponential demand abstract we introduce a novel strategy to address the issue of demand estimation in single item single period stochastic inventory optimisation problems our strategy analytically combines confidence interval analysis and inventory optimisation we assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that with prescribed confidence probability includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter s in addition for each candidate order quantity that is identified our approach produces an upper and a lower bound for the associated cost we apply this approach to three demand distributions in the exponential family binomial poisson and exponential for two of these distributions we also discuss the extension to the case of unobserved lost sales numerical examples are presented in which we show how our approach complements existing frequentist e g based on maximum likelihood estimators or bayesian strategies

learning experimentation and the optimal output decisions of a competitive firm this paper considers the effect of learning from experience on the output decisions of a perfectly competitive firm faced with the demand uncertainty specifically a bayesian framework for expectations formation and demand forecasting by a perfectly competitive firm is presented focusing the analysis on the determination of optimal sequential output decisions it is shown that through output experimentation the experimenting firm will select a non myopic sequential policy and will tend to overproduce the exact magnitude of the overproduction and the economic value of experimentation are contingent upon model parameters and the length of the planning horizon

the pension costs from a defined benefit to individual pension accounts do they cost more in the case of taiwan this article develops a market based liability valuation model to price individual pension costs of a defined benefit db pension plan the purpose is to compare them with the new labour pension plan individual pension accounts ipas in the case of taiwan the results based on the numerical approach show that the new ipas cost a company more than the old db plan except if the average wage growth relative to the risk free interest rate is high enough

the valuation of multiple claim insurance contracts this paper provides a closed form solution for the value of a multiple claim insurance contract that is subject to a deductible amount and or an upper limit on claims the solution is a time integral of european option prices the model provides three important insights first systematic risk in insurance policies is altered in the presence of deductibles and maximum indemnity levels second idiosyncratic risk affects policy valuation and the required rates of return on underwriting portfolios finally contrary to traditional actuarial intuition changes in the risk free interest rate may either increase or reduce policy values

observation bias the impact of demand censoring on newsvendor level and adjustment behavior in an experimental newsvendor setting we investigate three phenomena level behavior the decision maker s average ordering tendency adjustment behavior the tendency to adjust period to period order quantities and observation bias the tendency to let the degree of demand feedback influence order quantities we find that in three of four conditions the portion of mismatch cost that results from adjustment behavior exceeds the portion of mismatch cost caused by level behavior observation bias is studied through censored demand feedback a situation that arguably represents most newsvendor settings when demands are uncensored subjects tend to order below the normative quantity when they face high margin and above the normative quantity when they face low margin but in neither case do they order beyond mean demand the pull to center effect censoring in general leads to lower quantities magnifying the below normative level behavior when they face high margin but partially counterbalancing the above normative level behavior when they face low margin violating the pull to center effect in both cases data as supplemental material are available at http dx doi org 10 1287 mnsc 2013 1825 this paper was accepted by christian terwiesch operations management

statistical learning of service dependent demand in a multiperiod newsvendor setting we study an inventory system wherein a customer may leave the seller s market after experiencing an inventory stockout traditionally researchers and practitioners assume a single penalty cost to model this customer behavior of stockout aversion recently a stream of researchers explicitly model this customer behavior and support the traditional penalty cost approach we enrich this literature by studying the statistical learning of service dependent demand we build and solve four models a baseline model where the seller can observe the demand distribution a second model where the seller cannot observe the demand distribution but statistically learns the demand distribution a third model where the seller can learn or pay to obtain the exact information of the demand distribution and a fourth model where demand in excess of available inventory is lost and unobserved interestingly we find that all four models support the traditional penalty cost approach this result confirms the use of a state independent stockout penalty cost in the presence of demand learning more strikingly the first three models imply the same stockout penalty cost which is larger than the stockout penalty cost implied by the last model

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

bayes solution to dynamic inventory models under unknown demand distribution this paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate

on the censored newsvendor and the optimal acquisition of information we have read ding et al 2002 referred to hereafter as dpb with great interest dpb con ains two main results theorem a claims that the myopic inventory level is a lower bound on the optimal inventory level and theo rem b attempts to quantify the marginal expected value of information however there are mistakes in the proof of theorem a the result itself is correct a proof is given in lu et al 2004 furthermore one of the erroneous expressions in dpb s proof leads to an error in the marginal expected value of information in theorem b we now provide more details the equation numbers unless specified otherwise refer to the appendix of dpb available at the operations research home page http or pubs informs org the main error in the proof of theorem a is the follow ing if a x and b x are two functions of the variable jc then the derivative of a x b x with respect to x is d r x m da x db x a x b x b x a x dpb s mistake in essence is to omit the second term more specifically a key step in proving theorem a is inequality 35

the censored newsvendor and the optimal acquisition of information this paper investigates the effect of demand censoring on the optimal policy in newsvendor inventory models with general parametric demand distributions and unknown parameter values we show that the newsvendor problem withobservable lost sales reduces to a sequence of single period problems while the newsvendor problem withunobservable lost sales requires a dynamic analysis using a bayesian markov decision process approach we show that the optimalin ventory level in the presence of censored demand ishigher than would be determined using a bayesian myopic policy we explore the economic rationality for this observation and illustrate it with numerical examples

demand estimation and ordering under censoring stock out timing is almost all you need retailers facing uncertain demand can use observed sales to update demand estimates however such learning is limited by the amount of inventory carried when demand exceeds inventory i e when a stock out event occurs a retailer in general cannot observe actual demand we propose using observations on the timing of sales occurrences in a bayesian fashion to learn about demand and we analyze this learning method for a multiperiod newsvendor setting we find that as previously shown with the use of only stock out event observations the optimal order quantity with timing observations is greater than the optimal order quantity with full demand observations we prove this result using a novel methodology from the statistics literature on comparison of experiments although the optimal over ordering with timing observations tends to be less than that with only stock out event observations in most cases we do observe cases where the opposite is true such cases correspond to high demand uncertainty and low margins where marginal learning from timing observations is significantly higher than using only a stock out event in an extensive numerical study we find that on average and with respect to uncensored demand observations the use of timing observations eliminates 76 1 of the loss in expected profit from using only stock out event observations we show that for poisson and normal demand with unknown mean the proposed learning method is tractable as well as intuitively appealing the information contained in the timing of sales occurrences is fully captured by a single number the timing of stock out we also investigate checkpoint models in which the newsvendor can make observations only at predetermined times in a period and illustrate its convergence to the models with timing and stock out event observations

optimal inventory decisions in a multiperiod newsvendor problem with partially observed markovian supply capacities abstract this paper considers a multi period news vendor problem with partially observed supply capacity information which evolves as a markovian process the supply capacity is fully observed by the buyer when the capacity is smaller than the buyer s ordering quantity otherwise the buyer knows that the current period supply capacity is greater than its ordering quantity based on these two observations the buyer updates the future supply capacity forecasting accordingly with a dynamic programming formulation we prove the existence of an optimal ordering policy we also prove that the optimal order quantity is greater than the myopic order quantity

adaptive data driven inventory control with censored demand based on kaplan meier estimator using the well known product limit form of the kaplan meier estimator from statistics we propose a new class of nonparametric adaptive data driven policies for stochastic inventory control problems we focus on the distribution free newsvendor model with censored demands the assumption is that the demand distribution is not known and there are only sales data available we study the theoretical performance of the new policies and show that for discrete demand distributions they converge almost surely to the set of optimal solutions computational experiments suggest that the new policies converge for general demand distributions not necessarily discrete and demonstrate that they are significantly more robust than previously known policies as a by product of the theoretical analysis we obtain new results on the asymptotic consistency of the kaplan meier estimator for discrete random variables that extend existing work in statistics to the best of our knowledge this is the first application of the kaplan meier estimator within an adaptive optimization algorithm in particular the first application to stochastic inventory control models we believe that this work will lead to additional applications in other domains

learning consumer tastes through dynamic assortments how should a firm modify its product assortment over time when learning about consumer tastes in this paper we study dynamic assortment decisions in a horizontally differentiated product category for which consumers diverse tastes can be represented as locations on a hotelling line we presume that the firm knows all possible consumer locations comprising a finite set but does not know their probability distribution we model this problem as a discrete time dynamic program each period the firm chooses an assortment and sets prices to maximize the total expected profit over a finite horizon given its subjective beliefs over consumer tastes the consumers then choose a product from the assortment that maximizes their own utility the firm observes sales which provide censored information on consumer tastes and it updates beliefs in a bayesian fashion there is a recurring trade off between the immediate profits from sales in the current period exploitation and the informational gains to be exploited in all future periods exploration we show that one can partially order assortments based on their information content and that in any given period the optimal assortment cannot be less informative than the myopically optimal assortment this result is akin to the well known stock more result in censored newsvendor problems with the newsvendor learning about demand through sales when lost sales are not observable we demonstrate that it can be optimal for the firm to alternate between exploration and exploitation and even offer assortments that lead to losses in the current period in order to gain information on consumer tastes we also develop a bayesian conjugate model that reduces the state space of the dynamic program and study value of learning using this conjugate model

central bank intervention and exchange rate volatility abstract this paper explores the effects of foreign exchange intervention by central banks on the behavior of exchange rates the g 3 central banks have undertaken an unprecedented number of both coordinated and unilateral intervention operations in the last 10 years existing empirical evidence on the effectiveness of intervention is mixed studies using data from the 1970s suggest that intervention operations that do not affect the monetary base have at most a short lived influence on exchange rates but more recent studies indicate that the intervention operations that followed the plaza agreement influenced both the level and variance of exchange rates this paper examines the effects of us german and japanese monetary and intervention policies on dollar mark and dollar yen exchange rate volatility over the 1977 1994 period the results indicate that intervention operations generally increase exchange rate volatility this is particularly true of secret interventions which are those undertaken by central banks without notification of the public overt interventions in the mid 1980s appear to have reduced exchange rate volatility but in other periods and for the 1977 1994 period as a whole central bank intervention is associated with greater exchange rate volatility

the portable guarantee to exchange back an old defined benefit for a new defined contribution dc pension plan as a defined contribution dc pension plan is introduced to replace a defined benefit db pension plan the portability benefit from a dc pension plan costs the employees to bear the investment risk from managing the pension fund to protect the retirement income and maintain the portability benefit a guarantee to exchange back the old defined benefit is supposed to be demanded for the new dc plan s participants in the guarantee market in light of such a demand this article applies a claim terminating insurance pricing model to offer a contingent claims pricing model for a portable pension guarantee using the new labor pension plan of taiwan as an illustration a guaranteed dc pension will carry an extra cost of almost 50 up to over 100 of the plan s contributions over the participant s work life given the current mandatory minimum requirement of a contribution rate of 6

stalking information bayesian inventory management with unobserved lost sales retailers are frequently uncertain about the underlying demand distribution of a new product when taking the empirical bayesian approach of scarf 1959 they simultaneously stock the product over time and learn about the distribution assuming that unmet demand is lost and unobserved this learning must be based on observing sales rather than demand which differs from sales in the event of a stockout using the framework and results of braden and freimer 1991 the cumulative learning about the underlying demand distribution is captured by two parameters a scale parameter that reflects the predicted size of the underlying market and a shape parameter that indicates both the size of the market and the precision with which the underlying distribution is known an important simplification result of scarf 1960 and azoury 1985 which allows the scale parameter to be removed from the optimization is shown to extend to this setting we present examples that reveal two interesting phenomena 1 a retailer may hope that compared to stocking out realized demand will be strictly less than the stock level even though stocking out would signal a stochastically larger demand distribution and 2 it can be optimal to drop a product after a period of successful sales we also present specific conditions under which the following results hold 1 investment in excess stocks to enhance learning will occur in every dynamic problem and 2 a product is never dropped after a period of poor sales the model is extended to multiple independent markets whose distributions depend proportionately on a single unknown parameter we argue that smaller markets should be given better service as an effective means of acquiring information

the equilibrium valuation of risky discrete cash flows in continuous time this paper values a contingent claim to discrete stochastic cash flows generated by a poisson arrival process with a randomly varying intensity parameter in the most general case both the size and the arrival intensity of cash flows may correlate wih state variables in a continuous time economy assuming the conditions of an intertemporal capital aset pricing model solutions for the value of the contingent claim can be found using various techniques the paper suggests immediate applications to the valuation of insurance contracts the decision to build a firm with unknown future investment opportunities and the pricing of mortgage backed securities

rear view mirror driving in defined contribution systems the strange formula of the chilean pension funds the pioneering regulation on chilean pension funds under defined contribution program requires private managing institutions to exclusively manage individual accounts and meet a minimum return to their clients the purpose of this study is to empirically investigate the investment behaviour of pension funds and to contribute to the social security debate the findings reveal the benchmark significantly explains funds performance pension funds tend to replicate their asset allocations to exhibit similarities in returns we believe the obligation on fund managers to attain a minimum guaranteed return based on relative performance evaluation encourages them not to deviate from the industry s performance indeed the benchmark explains most of the group performance to hold similar allocations managers may monitor each others through their investment style

myopic policies for some inventory models with uncertain demand distributions the majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty while this assumption is unsupported in many applied contexts it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies this paper shows that a simple inventory policy based upon a critical fractile can be optimal or near optimal in some inventory models with parameter adaptive demand processes in these some parameter of the demand distribution is not known with certainty and estimates of the parameter are updated in a statistical fashion as demand is observed through time examples include exponentially smoothed forecasts and bayesian updating of parameter estimates bounds on the value loss relative to optimal cost when using the critical fractile policy can be calculated directly from the problem data some numerical examples illustrate the technique

intramarginal intervention in the ems and the target zone model of exchange rate behavior abstract exchange rate data produced by the european monetary system ems contradict important predictions made by the standard target zone model we show that the contradictions reflect a misinterpretation of policies pursued by the ems countries they intervened intramarginally to keep exchange rates will within their bands not at the edges of the bands to keep rates from crossing them in the basle nyborg agreement of 1987 however they agreed to make fuller use of the band and exchange rates behave differently thereafter the effect appears clearly in the behavior of the french franc and less decisively in the behavior of the italian lira we conclude by examining and rejecting other explanations for the observed difference in exchange rate behavior

multi period inventory games with information update this paper addresses the multi period inventory game of two substitutable products with learning in which the demand distribution form in each period is known but one or more parameters are unknown in advance the retailers update the estimates of the unknown parameters using the historical demand information as the transaction proceeds at each period the retailers check the initial inventories and update the forecasts about their demands first then they place the orders which are delivered immediately finally the demands are realized and satisfied by the available inventories the unsatisfied demand of one retailer switches to another and is satisfied by the other s left inventory unsatisfied demand is lost and the excess inventories incur a holding cost all the information is common knowledge the objectives of the two retailers are to make proper ordering decisions to maximize their total expected discount profits respectively we model the problem as a dynamic bayesian game with multi dimension state space we give the conditions under which the state space can be reduced we prove the existence and uniqueness of nash equilibrium and show that the equilibrium ordering strategy is the base stock policy the computation of the base stock levels can be reduced to a game with one dimension state space moreover for the case with perishable product the computation of the base stock levels can be reduced to the newsboy game