Hybrid is good: stochastic optimization and applied statistics for or

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Chun, So Yeon
Kleywegt, Anton J.
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In the first part of this thesis, we study revenue management in resource exchange alliances. We first show that without an alliance the sellers will tend to price their products too high and sell too little, thereby foregoing potential profit, especially when capacity is large. This provides an economic motivation for interest in alliances, because the hope may be that some of the foregone profit may be captured under an alliance. We then consider a resource exchange alliance, including the effect of the alliance on competition among alliance members. We show that the foregone profit may indeed be captured under such an alliance. The problem of determining the optimal amounts of resources to exchange is formulated as a stochastic mathematical program with equilibrium constraints. We demonstrate how to determine whether there exists a unique equilibrium after resource exchange, how to compute the equilibrium, and how to compute the optimal resource exchange. In the second part of this thesis, we study the estimation of risk measures in risk management. In the financial industry, sell-side analysts periodically publish recommendations of underlying securities with target prices. However, this type of analysis does not provide risk measures associated with underlying companies. In this study, we discuss linear regression approaches to the estimation of law invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of the standard least squares method and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, Value-at-Risk and Average Value-at-Risk measures are discussed in detail. Large sample statistical inference of the estimators is derived. Furthermore, finite sample properties of the proposed estimators are investigated and compared with theoretical derivations in an extensive Monte Carlo study. Empirical results on the real data (different financial asset classes) are also provided to illustrate the performance of the estimators.
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