Relative entropy, exponential utility, and robust dynamic pricing
成果类型：
Article
署名作者：
Lim, Andrew E. B.; Shanthikumar, J. George
署名单位：
University of California System; University of California Berkeley
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0385
发表日期：
2007
页码：
198-214
关键词：
摘要：
In the area of dynamic revenue management, optimal pricing policies are typically computed on the basis of an underlying demand rate model. From the perspective of applications, this approach implicitly assumes that the model is an accurate representation of the real-world demand process and that the parameters characterizing this model can be accurately calibrated using data. In many situations, neither of these conditions are satisfied. Indeed, models are usually simplified for the purpose of tractability and may be difficult to calibrate because of a lack of data. Moreover, pricing policies that are computed under the assumption that the model is correct may perform badly when this is not the case. This paper presents an approach to single-product dynamic revenue management that accounts for errors in the underlying model at the optimization stage. Uncertainty in the demand rate model is represented using the notion of relative entropy, and a tractable reformulation of the robust pricing problem is obtained using results concerning the change of probability measure for point processes. The optimal pricing policy is obtained through a version of the so-called Isaacs' equation for stochastic differential games, and the structural properties of the optimal solution are obtained through an analysis of this equation. In particular, (i) closed-form solutions for the special case of an exponential nominal demand rate model, (ii) general conditions for the exchange of the max and the min in the differential game, and (iii) the equivalence between the robust pricing problem and that of single-product revenue management with an exponential utility function without model uncertainty, are established through the analysis of this equation.