Dynamic Pricing with Stochastic Reference Price Effect

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  • 1 Department of Industrial Enterprise and Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;
    2 NUS Business School, National University of Singapore, Singapore 119245, Singapore;
    3 Two Sigma Investments, New York, NY 10036, USA

Received date: 2018-01-20

  Revised date: 2018-07-21

  Online published: 2019-03-30

Supported by

This research is partly supported by the National Science Foundation (Nos. CMMI-1030923, CMMI-1363261, CMMI-1538451 and CMMI-1635160), the National Natural Science Foundation of China (Nos. 71228203, 71201066 and 71520107001), and research Grant of National University of Singapore (Project R-314-000-105-133).

Abstract

We study a dynamic pricing problem of a firm facing stochastic reference price effect. Randomness is incorporated in the formation of reference prices to capture either consumers' heterogeneity or exogenous factors that affect consumers' memory processes. We apply the stochastic optimal control theory to the problem and derive an explicit expression for the optimal pricing strategy. The explicit expression allows us to obtain the distribution of the steady-state reference price. We compare the expected steadystate reference price to the steady-state reference price in a model with deterministic reference price effect, and we find that the former one is always higher. Our numerical study shows that the two steady-state reference prices can have opposite sensitivity to the problem parameters and the relative difference between the two can be very significant.

Cite this article

Xin Chen, Zhen-Yu Hu, Yu-Han Zhang . Dynamic Pricing with Stochastic Reference Price Effect[J]. Journal of the Operations Research Society of China, 2019 , 7(1) : 107 -125 . DOI: 10.1007/s40305-018-0227-1

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