Robust Dynamic Pricing over Infinite Horizon in the Presence of Model Uncertainty
Robust Dynamic Pricing over Infinite Horizon in the Presence of Model Uncertainty
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DOI：
10.1142/s021759590900247x
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发表时间：
2009-12
期刊：
影响因子：
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通讯作者：
Gendao Li;Y. Xiong;Zhongkai Xiong
中科院分区：
文献类型：
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作者：
Gendao Li;Y. Xiong;Zhongkai Xiong
研究了库存有限、需求率模型不确定、目标是在无限时间范围内最大化期望折扣收益的零售商动态定价问题。这家零售商怀疑他的需求模型，该模型是由历史数据生成的，并将其视为近似值。需求速率模型中的不确定性用广义相对熵过程来表示，稳健定价问题被描述为一个两人零和随机微分博弈。定价策略通过Hamilton-Jacobi-Isaacs(HJI)方程得到。证明了HJI方程解的存在唯一性，并证明了一个验证定理，证明了HJI方程的解确实是定价问题的价值函数。并以指数名义需求率为例进行了验证。
This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.