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

Xiaowei Xu () and Wallace J. Hopp ()
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Xiaowei Xu: Department of Supply Chain Management and Marketing Sciences, Rutgers, The State University of New Jersey, Newark, New Jersey 07102
Wallace J. Hopp: Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109

Operations Research, 2009, vol. 57, issue 5, 1298-1302

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.

Keywords: probability; stochastic model applications (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (9)

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