ROBUST DYNAMIC PRICING OVER INFINITE HORIZON IN THE PRESENCE OF MODEL UNCERTAINTY

Gendao Li (), Yu Xiong () and Zhongkai Xiong ()
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Gendao Li: School of Economics and Business Administration, Chongqing University, Chongqing 400030, China
Yu Xiong: Queen's University Management School, 25 University Square, Belfast, BT7 1NN, UK
Zhongkai Xiong: School of Economics and Business Administration, Chongqing University, Chongqing 400030, China

Asia-Pacific Journal of Operational Research (APJOR), 2009, vol. 26, issue 06, 779-804

Abstract: This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

Keywords: Dynamic pricing; revenue management; discounted relative entropy; robust control (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S021759590900247X

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