Joline Uichanco

Tractable Robust Expected Utility and Risk Models for Portfolio Optimization

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst-case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box-type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst-case risk under distributional ambiguity. New closed-form results for the worst-case optimized certainty equivalent risk measures and optimal portfolios are provided for two- and three-piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.

The Data-Driven Newsvendor Problem: New Bounds and Insights

Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation SAA approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments. This bound reveals that the demand distributions weighted mean spread affects the accuracy of the SAA heuristic.

Asymmetry and Ambiguity in Newsvendor Models

A basic assumption of the classical newsvendor model is that the probability distribution of the random demand is known. But in most realistic settings, only partial distribution information is available or reliably estimated. The distributionally robust newsvendor model is often used in this case where the worst-case expected profit is maximized over the set of distributions satisfying the known information, which is usually the mean and covariance of demands. However, covariance does not capture information on asymmetry of the demand distribution. In this paper, we introduce a measure of distribution asymmetry using second-order partitioned statistics. Semivariance is a special case with a single partition of the univariate demand. With mean, variance, and semivariance information, we show that a three-point distribution achieves the worst-case expected profit and derive a closed-form expression for the distributionally robust order quantity. For multivariate demand, the distributionally robust problem ...

Inventory Optimization for Fulfillment Integration in Omnichannel Retailing

With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an integrated omnichannel approach. Such integration can lead to reduction in cost that can be achieved through efficient inventory management. A retailer with a network of physical stores and fulfillment centers facing two demands (online and in-store) has to make important, interlinked decisions - how much inventory to keep at each location and where to fulfill each online order from, as online demand can be fulfilled from any location. We consider order-up-to policies for a general multi-period model with multiple locations and zero lead time, and online orders fulfilled multiple times in each period. We first focus on the case where fulfillment decisions are made at the end of each period, which allows separate focus on the inventory decision. We develop a simple, scalable heuristic for the multi-location problem based on analysis from the two-store case, and prove its asymptotic near-optimality for large number of omnichannel stores under certain conditions. We extend this to the case where fulfillment is done multiple times within a period and combine it with a simple, threshold-based fulfillment policy which reserves inventory at stores for future in-store demand. With the help of a realistic numerical study based on a fictitious retail network embedded in mainland USA, we show that the combined heuristic outperforms a myopic, decentralized planning strategy under a variety of problem parameters, especially when there is an adequate mix of online and in-store demands. Extensions to positive lead times are discussed.With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration , ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.