Dynamic Pricing with Stochastic Reference Price Effect

Xin Chen, Zhen Yu Hu, Yu Han Zhang

Research output: Contribution to journalArticlepeer-review


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 steady-state 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.

Original languageEnglish (US)
Pages (from-to)107-125
Number of pages19
JournalJournal of the Operations Research Society of China
Issue number1
StatePublished - Mar 6 2019


  • Dynamic pricing
  • Reference price effect
  • Stochastic optimal control

ASJC Scopus subject areas

  • Mathematics(all)
  • Management Science and Operations Research
  • Applied Mathematics


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