Robust timing decisions with applications in finance and revenue management.

摘要

In this dissertation we investigate robust optimization techniques for timing decisions in revenue management and finance. Our main contribution is to develop optimization models for decision times under uncertainty that require little information on the probability distribution, have an adjustable level of conservatism to ensure performance, and allow us to study how time affects the structure of the optimal policy in finance and revenue management problems. The managerial insights gained from our models assist a decision-maker determine his optimal strategy in settings where limited recourse is available when the manager has implemented his decision, such as putting items on sale, increasing plant capacity, or selling a stock.;Specifically, in the first part of this dissertation, we analyze how robust optimization can be used to develop a modeling framework to address timing decisions in revenue management. In a robust pricing setting, where the objective is to maximize revenue, the main properties of the optimal solution are the optimal sale time and optimal prices to sell units under uncertain demand. We explore the advantages of linear, as opposed to non-linear, robust formulations for a single product and address the tractability of the two approaches. We study the properties of a piecewise linear approximation to a non-linear, non-convex problem in the case of a concave budget of uncertainty, and introduce a heuristic to cut down the complexity of solving the problem. We then describe how to use the solution of the static robust optimization model to implement a dynamic markdown policy. The case of multiple resources is also considered, where we suggest the idea of constraint aggregation to preserve performance. In a robust capacity expansion setting, we address uncertain demand using robust linear optimization with polyhedral uncertainty sets in the presence of a nonconvex piecewise linear objective function. We compute the optimal timing and level of capacity expansion, which represent the main properties of the optimal policy. We show that the worst-case problem is equivalent to a deterministic problem with modified parameters. Further, we develop a technique to iteratively generate extreme points of the feasible set that reduces the size of the problem to be solved, and generally solves the general robust problem much faster.;In the second part, we analyze how robust optimization techniques can be used to incorporate risk aversion in two important finance problems. We rely on existing robust optimization concepts, and demonstrate how these concepts can be implemented in a dynamic setting. First, we present a simple, intuitive approach to compute the optimal allocation across multiple asset classes in a portfolio management setting that captures market volatility, length of time horizon and investors' risk preferences. It extends the allocation rules traditionally used in retirement planning and allows the investor to observe easily the impact of his decision parameters on the optimal policy. Then, in a robust selling times problem, we propose an approach to dynamic portfolio management based on the sequential update of stock price forecasts in a robust optimization setting, where the updating process is driven by the historical observations. We model uncertainty on stock returns through downside probability thresholds, and allow actual price movements to drive decisions.