In many real-life situations, the inventory record may not match the actual stock perfectly. This can happen due to distortion of inventory data, such as transaction errors, misplaced inventories, and spoilage. In these cases, because the decision maker only has incomplete information about the inventory levels, many well-known inventory policies are not even admissible, and our understanding of the optimal policies, even their existence, is very limited. In “Average Cost Optimality in Partially Observable Lost-Sales Inventory Systems,” Bai et al. consider the classical lost-sales inventory model, in which the inventory level is only observed when it becomes zero. They formulate the cost-minimization problem as a partially observable Markov decision process. By exploiting the vanishing discount factor approach, they provide a way to verify the existence of optimal policies under the average cost criterion. The key step in their analysis is the construction of a valid policy, which, in a certain sense, copies the actions of another policy for the process starting from another initial state.

Average Cost Optimality in Partially Observed Lost-Sales Inventory Systems

Hedge fund strategies, performance &diversification: A portfolio theory & stochastic discount factor approach

We consider average-cost Markov decision processes (MDPs) with Borel state and action spaces and universally measurable policies. For the nonnegative cost model and an unbounded cost model with a Lyapunov-type stability character, we introduce a set of new conditions under which we prove the average cost optimality inequality (ACOI) via the vanishing discount factor approach. Unlike most existing results on the ACOI, our result does not require any compactness and continuity conditions on the MDPs. Instead, the main idea is to use the almost-uniform-convergence property of a pointwise convergent sequence of measurable functions as asserted in Egoroff's theorem. Our conditions are formulated in order to exploit this property. Among others, we require that for each state, on selected subsets of actions at that state, the state transition stochastic kernel is majorized by finite measures. We combine this majorization property of the transition kernel with Egoroff's theorem to prove the ACOI.

Hedge Fund Strategies, Performance & Diversification: A Portfolio Theory & Stochastic Discount Factor Approach

ABSTRACTIn the short run, there can be substantial differences in spot freight earnings between geographical regions of the global freight market for bulk carriers. Such differences can be consistent with an efficient market if they are temporary and if they cannot be exploited financially by pursuing chartering strategies that are based on publicly available information. In this paper, we apply a simple optimal switching model to evaluate whether such chartering strategies exist. We model the spot freight rate differential between the Atlantic and Pacific basins as a mean-reverting Ornstein–Uhlenbeck process and the entry–exit decision using the discount factor approach, which results in optimal trigger values for the entry/exit from each basin. Our empirical results suggest that the market is spatially efficient during normal freight market conditions when there is a surplus of vessels. The tight market conditions during the 2003–2008 freight market boom caused a persistent upward bias in Atlantic freight rates, but also here we find little added value from pursuing an active switching strategy.

Dual-sourcing inventory systems, in which one supplier is faster (i.e., express) and more costly, while the other is slower (i.e., regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize because of the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called tailored base-surge (TBS) policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the express source follows a simple order-up-to rule. Numerical experiments by several authors have suggested that such policies perform well as the lead time difference between the two sources grows large, which is exactly the setting in which the curse of dimensionality leads to the problem becoming intractable. However, providing a theoretical foundation for this phenomenon has remained a major open problem. In this paper, we provide such a theoretical foundation by proving that a simple TBS policy is indeed asymptotically optimal as the lead time of the regular source grows large, with the lead time of the express source held fixed. Our main proof technique combines novel convexity and lower-bounding arguments, an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes, and ideas from the theory of random walks and queues, significantly extending the methodology and applicability of a novel framework for analyzing inventory models with large lead times recently introduced by Goldberg and coauthors in the context of lost-sales models with positive lead times. This paper was accepted by Gad Allon, operations management.

Can Stochastic Discount Factor Models Explain the Cross Section of Equity Returns?

An Empirical Study on the Stock Price Reaction to Earnings Announcements using the Stochastic Discount Factor Approach

On the vanishing discount factor approach for Markov decision processes with weakly continuous transition probabilities

Are good-news firms riskier than bad-news firms?

Executive Stock Options Pricing with Free Wealth Weights and Continuous Partial Exercise: An Analytic Constrained Portfolio Optimization/Stochastic Discount Factor Approach

We employ mean‐variance spanning and intersection tests in the stochastic discount factor approach to examine the potential diversification benefits of international investments from the perspective of Korean investors. Our results show that the addition of international regional indices to the set of domestic equities provides significant diversification benefits. However, the source and economic magnitude of diversification benefits differ across international markets. Furthermore, we find that when investors manage their portfolio based on instrument variables, they can not only expand their investment opportunities by investing in international assets, but also increase the efficiency gain of diversification benefits.

Empirical estimation in average Markov control processes

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.

Portfolio Efficiency and Discount Factor Bounds with Conditioning Information: An Empirical Study

Bond Pricing and Basis Risk when the Short Term Interest Rate Follows a Threshold Process

Bond Pricing When the Short Term Interest Rate Follows a Threshold Process

Entry and exit decisions based on a discount factor approach

Abstract We examine the performance of U.K. unit trusts between January 1982 and December 1996 within the stochastic discount factor approach across a wide class of models. No one model dominates the others in correctly pricing passive portfolios or detecting superior performance for hypothetical trading strategies. We find no evidence of significant superior performance by the unit trusts for any model of the stochastic discount factor. Also, the charges of the trust have a mixed effect on trust performance.