an extended production recycling model with stationary demand and return rates abstract a production recycling system is investigated a constant demand can be satisfied with production and recycling the used items are bought back and then recycled the non recycled products are disposed of two types of models will be analyzed the first model examines the eoq related costs and minimizes the relevant costs the second model generalizes the first model with the introduction of the cost function with linear waste disposal recycling production and buyback costs it is asked whether the pure either production or recycling or mixed strategies are optimal and it will be shown that under these circumstances the mixed strategies are dominated by the pure strategies the paper generalizes a former model proposed by the authors for the case of one recycling and one production batch to the case of arbitrary batch numbers

on the structure of lost sales inventory models we provide a new approach to the structural analysis of the standard lost sales inventory system this approach is we think easier to work with than the original one we also derive new bounds on the optimal policy then we show that more variable demand leads to higher cost finally we extend the analysis to several important variations of the basic model

evaluating interval forecasts a complete theory for evaluating interval forecasts has not been worked out to date most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage consequently i set out to build a consistent framework for conditional interval forecast evaluation which is crucial when higher order moment dynamics are present the new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management

backtesting marginal expected shortfall and related systemic risk measures this paper proposes an original approach for backtesting systemic risk measures this backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the finan

bank capital regulation of trading portfolios an assessment of the basel framework in setting minimum capital requirements for trading portfolios the basel committee on banking supervision 1996 2011a 2013 initially used value at risk var then both var and stressed var svar and most recently stressed conditional var scvar accordingly we examine the use of scvar to measure risk and set these requirements assuming elliptically distributed asset returns we show that portfolios on the mean scvar frontier generally lie away from the mean variance m v frontier in a plausible numerical example we find that such portfolios tend to have considerably higher ratios of risk measured by e g standard deviation to minimum capital requirement than those of portfolios on the m v frontier also we find that requirements based on scvar are smaller than those based on both var and svar but exceed those based on just var finally we find that requirements based on scvar are less procyclical than those based on either var or both var and svar overall our paper suggests that the use of scvar to measure risk and set requirements is not a panacea

a comparison of the optimal costs of two canonical inventory systems we compare two inventory systems one in which excess demand is lost and the other in which excess demand is backordered both systems are reviewed periodically they experience the same sequence of identically and independently distributed random demands holding and shortage costs are considered the holding cost parameter is identical however the cost of a lost sale could be different from the per period cost of backlogging a unit sale when these costs are equal we prove that the optimal expected cost for managing the system with lost sales is lower when the cost of a lost sale is greater we establish a relationship between these parameters that ensures that the reverse inequality is true these results are useful for designing inventory systems we also introduce a new stochastic comparison technique in this paper

the level and quality of value at risk disclosure by commercial banks in this paper we study both the level of value at risk var disclosure and the accuracy of the disclosed var figures for a sample of us and international commercial banks to measure the level of var disclosures we develop a var disclosure index that captures many different facets of market risk disclosure using panel data over the period 1996 2005 we find an overall upward trend in the quantity of information released to the public we also find that historical simulation is by far the most popular var method we assess the accuracy of var figures by studying the number of var exceedances and whether actual daily vars contain information about the volatility of subsequent trading revenues unlike the level of var disclosure the quality of var disclosure shows no sign of improvement over time we find that var computed using historical simulation contains very little information about future volatility

learning by doing and investment in training a synthesis of two rival models of the life cycle this paper provides a theoretical synthesis of recent discussions of learning by doing and investment in training as alternative forms of human capital accumulation these theoretical notions relate to essentially different phenomena in particular pace becker and mincer investment in training does not completely encompass learning by doing the paper then develops a model in which human capital accumulation occurs via both training and learning by doing the joint training learning model since it is more general then pure models in which all accumulation occurs via either training or learning avoids certain restrictive and seemingly implausible implications of either kind of pure model however the joint model also has implications that while compatible with stylized facts about the life cycle are sharper than those of either kind of pure model for example the joint model implies that market time and earnings must rise early in the life cycle while neither pure model without corners does so finally the notion of learning by doing provides a rationale for an empirical finding that has recently received attention to the effect that the rate of depreciation of human capital is not constant but rather depends on the extent to which it is used in market activities

closing the gap a learning algorithm for lost sales inventory systems with lead times we consider a periodic review single product inventory system with lost sales and positive lead times under censored demand in contrast to the classical inventory literature we assume the firm d

bank risk dynamics and distance to default we adapt structural models of default risk to take into account the special nature of bank assets the usual assumption of log normally distributed asset values is not appropriate for banks typical bank assets are risky debt claims which implies that they embed a short put option on the borrowers assets leading to a concave payoff this has important consequences for banks risk dynamics and distance to default estimation due to the payoff non linearity bank asset volatility rises following negative shocks to borrower asset values as a result standard structural models in which the asset volatility is assumed to be constant can severely understate banks default risk in good times when asset values are high bank equity payoffs resemble a mezzanine claim rather than a call option bank equity return volatility is therefore much more sensitive to big negative shocks to asset values than in standard structural models

asymptotic optimality of order up to policies in lost sales inventory systems we study a single product single location inventory system under periodic review where excess demand is lost and the replenishment lead time is positive the performance measure of interest is the long run average holding cost and lost sales penalty cost for a large class of demand distributions we show that when the lost sales penalty becomes large compared to the holding cost the relative difference between the cost of the optimal policy and the best order up to policy converges to zero for any given cost parameters we establish a bound on this relative difference numerical experiments show that the best order up to policy performs well yielding an average cost that is within 1 5 of the optimal cost when the ratio between the lost sales penalty and the holding cost is 100 we also propose a heuristic order up to level using two newsvendor expressions in our experiments the cost of this order up to policy is 2 52 higher on an average than the best order up to policy

inventory cost rate functions with nonlinear shortage costs this article considers five cost rate models for inventory control each summarizing the expected holding and shortage costs per period as a function of the inventory position all models have linear holding costs and shortage cost coefficients of dimension unit period unit and period the latter two coeficients may be the shadow costs of a fill rate and a ready rate service constraint respectively one of the cost rate models is a new suggestion intended to facilitate modeling of periodic review inventory systems if and only if conditions on the demand process are presented for which the cost rate is quasi convex in the inventory position the typical sufficient condition requires that the cumulative demand distribution be logconcave a condition that is met by most demand distributions commonly used in the inventory literature the results simplify optimization and extend the known optimality of s s and nq r policies to cost structures common in applications and to the presence of typical service constraints as a prerequisite for the study a series of new monotonicity results are derived for compound renewal processes

modeling financial contagion using mutually exciting jump processes we propose a model to capture the dynamics of asset returns with periods of crises that are characterized by contagion in the model a jump in one region of the world increases the intensity of jumps both in the same region self excitation as well as in other regions cross excitation generating episodes of highly clustered jumps across world markets that mimic the observed features of the data we develop and implement moment based estimation and testing procedures for this model the estimates provide evidence of self excitation both in the us and the other world markets and of asymmetric cross excitation with the us market typically having more influence on the jump intensity of other markets than the reverse we propose filtered values of the jump intensities as a measure of market stress and examine their out of sample forecasting abilities

an econometric model of serial correlation and illiquidity in hedge fund returns the returns to hedge funds and other alternative investments are often highly serially correlated in sharp contrast to the returns of more traditional investment vehicles such as long only equity portfolios and mutual funds in this paper we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure i e investments in securities that are not actively traded and for which market prices are not always readily available for portfolios of illiquid securities reported returns will tend to be smoother than true economic returns which will understate volatility and increase risk adjusted performance measures such as the sharpe ratio we propose an econometric model of illiquidity exposure and develop estimators for the smoothing prole as well as a smoothing adjusted sharpe ratio for a sample of 908 hedge funds drawn from the tass database we show that our estimated smoothing coecien ts vary considerably across hedge fund style categories and may be a useful proxy for quantifying illiquidity exposure

inventory control in directed networks a note on linear costs we consider periodic review inventory control problems in directed networks primary examples of which are distribution systems and assembly systems external demand could occur at each node when inventory is insufficient to meet requirements at a node a portion of this demand is backordered and the remaining is lost external demands as well as lead times for inventory purchase assembly and transportation are stochastic in each period linear sales revenues and the following costs all linear are charged at each node a inventory purchase assembly transfer cost to receive inventory b holding cost c backorder cost and d lost sales cost when the objective function of interest is a discounted sum of profits over a finite planning horizon it is shown that the sales prices and the inventory purchase assembly transfer cost parameters can be assumed to be zero without loss of generality the result is proved for every realization of demands and lead times some extensions to these results are discussed during this process we also generalize the concept of echelon inventories to directed networks

model risk and capital reserves abstract we propose a procedure to take model risk into account in the computation of capital reserves this addresses the need to make the allocation of capital reserves to positions in given markets dependent on the extent to which reliable models are available the proposed procedure can be used in combination with any of the standard risk measures such as value at risk and expected shortfall we assume that models are obtained by usual econometric methods which allows us to distinguish between estimation risk and misspecification risk we discuss an additional source of risk which we refer to as identification risk by way of illustration we carry out calculations for equity and fx data sets in both markets estimation risk and misspecification risk together explain about half of the multiplication factors employed by the bank for international settlements bis

technical note inventory systems with a generalized cost model we study a single stage inventory system with a generalized shortage penalty cost that includes the following three components i a cost that is an increasing function of the number of backordered units in a period ii a fixed cost incurred for each period in which there is a backorder irrespective of how many units are backordered and finally iii a cost that is an increasing function of the number of periods a customer is backordered we show the problem can be transformed into one in which the backorder cost depends on the inventory position only then we present two sets of conditions the first one restricts our attention to a special case of the generalized penalty cost model while the second one restricts our attention to stationary demand models with some distributional assumptions under the first resp second set of conditions we show that the expected cost in a period can be expressed as a convex resp quasiconvex function of the after ordering inventory position we use this property to prove the optimality of order up to policies under both sets of conditions and discuss extensions to the cases where either a fixed ordering cost or a batch ordering constraint is present

robustness of order up to policies in lost sales inventory systems we study an inventory system under periodic review when excess demand is lost it is known huh et al 2009 that the best base stock policy is asymptotically optimal as the lost sales penalty cost parameter grows we now show that this result is robust in the following sense consider the base stock level which is optimal in a backordering system with a per unit per period backordering cost in which the backorder cost parameter is a function of the lost sales parameter in the original system then there is a large family of functions mapping the lost sales cost parameter to the backorder cost parameter such that the resulting base stock policy is asymptotically optimal we also demonstrate the robustness phenomenon through a second result we consider the base stock level which is optimal in a backordering system in which a unit of backorder is charged a penalty cost only once such a system has been studied by rosling we show that this base stock policy is also asymptotically optimal furthermore we show that a modification suggested by archibald of this base stock level also results in an asymptotically optimal policy finally we numerically test the performance of this heuristic policy for a wide spectrum of values for the lost sales penalty cost parameter and illustrate the superior performance of archibald s method

var seductive but dangerous value at risk var has gained rapid acceptance as a valuable approach to risk management not all vars are equal however a study of var techniques used by dealers and end users reveals that var calculations differ significantly for the same portfolio vars are extremely dependent on parameters data assumptions and methodology calculation of eight common vars for three hypothetical portfolios demonstrates the potentially seductive but dangerous nature of any single approach to risk management in sum although var and other quantitative techniques are necessary aspects of an effective risk management program they are not sufficient to control risk

the pernicious effects of contaminated data in risk management banks hold capital to guard against unexpected surges in losses and long freezes in financial markets the minimum level of capital is set by banking regulators as a function of the banks own estimates of their risk exposures as a result a great challenge for both banks and regulators is to validate internal risk models we show that a large fraction of us and international banks uses contaminated data when testing their models in particular most banks validate their market risk model using profit and loss p l data that include fees and commissions and intraday trading revenues this practice is inconsistent with the definition of the employed market risk measure using both bank data and simulations we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models moreover our estimates suggest that the use of contaminated data can significantly reduce market risk induced regulatory capital

backtesting trading risk of commercial banks using expected shortfall this paper uses saddlepoint technique to backtest the trading risk of commercial banks using expected shortfall it is found that four out of six us commercial banks have excessive trading risks monte carlo simulation studies show that the proposed backtest is very accurate and powerful even for small test samples more importantly risk managers can carry out the proposed backtest based on any number of exceptions so that incorrect risk models can be promptly detected before any further huge losses are realized

continuous review s s policies with lost sales a method is developed to calculate an s s policy that minimizes the average stationary cost in an inventory system with constant lead time fixed order cost linear holding cost per unit time linear penalty cost per unit short discrete compound poisson demand and lost sales it is assumed that at most one order is outstanding or equivalently that s s s the procedure is compared to several easier to compute approximate solutions including one that assumes backordering examples are given that reveal that although the backorder solution is different than the lost sales one the cost penalty of using it in the lost sales situation is small

the emperor has no clothes limits to risk modelling abstract this paper considers the properties of risk measures primarily value at risk var from both internal and external regulatory points of view it is argued that since market data is endogenous to market behavior statistical analysis made in times of stability does not provide much guidance in times of crisis in an extensive survey across data classes and risk models the empirical properties of current risk forecasting models are found to be lacking in robustness while being excessively volatile for regulatory use the var measure may give misleading information about risk and in some cases may actually increase both idiosyncratic and systemic risk

managing inventory with multiple products lags in delivery resource constraints and lost sales a mathematical programming approach this paper develops an order up tos inventory model that is designed to handle multiple items resource constraints lags in delivery and lost sales without sacrificing computational simplicity mild conditions are shown to ensure that the expected average holding cost and the expected average shortage cost are separable convex functions of the order up to levels we develop nonparametric estimates of these costs and use them in conjunction with linear programming to produce what is termed the lp policy the lp policy has two major advantages over traditional methods first it can be computed in complex environments such as the one described above and second it does not require an explicit functional form of demand something that is difficult to specify accurately in practice in two numerical experiments designed so that optimal policies could be computed the lp policy fared well differing from the optimal profit by an average of 2 20 and 1 84 respectively these results compare quite favorably with the errors incurred in traditional methods when a correctly specified distribution uses estimated parameters our findings support the effectiveness of this mathematical programming technique for approximating complex real world inventory control problems

an economic production and remanufacturing model with learning effects abstract managing inventory in reverse logistics has been receiving much attention in recent years one inventory problem that has been of interest to researchers is the production and remanufacturing model where used items are collected and remanufactured to satisfy customer demand the available models in the literature do not discuss the learning effects in production and remanufacturing processes this may not be true in industries where labour costs and learning costs are expensive by modelling these learning effects management may use established learning models to better utilize capacity manage inventories and coordinate production and distribution throughout the chain this paper extends the production remanufacture and waste disposal model by assuming learning to occur in both production and remanufacturing processes however this paper also assumes that improvements due to learning require capital investment mathematical models are developed numerical examples are provided and results are discussed

risk models at risk the experience from the global financial crisis has raised serious concerns about the accuracy of standard risk measures as tools for the quantification of extreme downward risks a key reason for this is that risk measures are subject to a model risk due e g to specification and estimation uncertainty while regulators have proposed that financial institutions assess the model risk there is no accepted approach for computing such a risk we propose a remedy for this by a general framework for the computation of risk measures robust to model risk by empirically adjusting the imperfect risk forecasts by outcomes from backtesting frameworks considering the desirable quality of var models such as the frequency independence and magnitude of violations we also provide a fair comparison between the main risk models using the same metric that corresponds to model risk required corrections

caviar conditional autoregressive value at risk by regression quantiles value at risk var has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes var is defined as the value that a portfolio will lose with a given probability over a certain time horizon usually one or ten days despite its conceptual simplicity its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions interpreting the var as the quantile of future portfolio values conditional on current information we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies such as normality or i i d returns the conditional autoregressive value at risk or caviar model moves the focus of attention from the distribution of returns directly to the behavior of the quantile we specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by koenker and bassett to determine the unknown parameters since the objective function is not differentiable we use a differential evolutionary genetic algorithm for the numerical optimization utilizing the criterion that each period the probability of exceeding the var must be independent of all the past information we introduce a new test of model adequacy the dynamic quantile test applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments