Technical Note---Price Trends in a Dynamic Pricing Model with Heterogeneous Customers: A Martingale Perspective

Authors:
Xiaowei Xu;Wallace J. Hopp
Affiliations:
Department of Supply Chain Management and Marketing Sciences, Rutgers, The State University of New Jersey, Newark, New Jersey 07102;Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109
Venue:
Operations Research
Year:
2009

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Abstract

This note describes probabilistic properties of optimal price sample paths in a dynamic pricing model with a finite horizon and limited stock. We assume that customer arrivals follow a nonhomogeneous Poisson process. We show that if customers' willingness-to-pay increases rapidly over time, then the optimal price process follows a submartingale, which implies an upward price trend. Alternatively, if customers' willingness-to-pay decreases rapidly over time, then the optimal price process follows a supermartingale, which implies a downward price trend.