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

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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)

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.

Suggested Citation

  • Xiaowei Xu & Wallace J. Hopp, 2009. "Technical Note---Price Trends in a Dynamic Pricing Model with Heterogeneous Customers: A Martingale Perspective," Operations Research, INFORMS, vol. 57(5), pages 1298-1302, October.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:5:p:1298-1302
    DOI: 10.1287/opre.1090.0703
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    References listed on IDEAS

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    Cited by:

    1. Sato, Kimitoshi, 2019. "Price Trends and Dynamic Pricing in Perishable Product Market Consisting of Superior and Inferior Firms," European Journal of Operational Research, Elsevier, vol. 274(1), pages 214-226.
    2. Choi, Tsan-Ming & Sethi, Suresh, 2010. "Innovative quick response programs: A review," International Journal of Production Economics, Elsevier, vol. 127(1), pages 1-12, September.
    3. Xiaowei Xu, 2009. "Optimal Price and Product Quality Decisions in a Distribution Channel," Management Science, INFORMS, vol. 55(8), pages 1347-1352, August.
    4. Kimitoshi Sato, 2021. "Dynamic pricing with automated purchase-reservation algorithms," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 20(1), pages 33-41, February.
    5. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    6. Yusen Xia & Jian Yang & Tingting Zhou, 2019. "Revenue management under randomly evolving economic conditions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 73-89, February.
    7. Desheng Wu, 2017. "Pass-through decision analysis in a supply chain," Annals of Operations Research, Springer, vol. 257(1), pages 297-316, October.
    8. Yuri Levin & Mikhail Nediak & Andrei Bazhanov, 2014. "Quantity Premiums and Discounts in Dynamic Pricing," Operations Research, INFORMS, vol. 62(4), pages 846-863, August.
    9. Wanyang Dai, 2022. "Optimal policy computing for blockchain based smart contracts via federated learning," Operational Research, Springer, vol. 22(5), pages 5817-5844, November.

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    probability; stochastic model applications;

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