基于贝叶斯信息更新的风险规避库存策略研究

Risk aversion in inventory management with Bayesian information updating

在贝叶斯库存控制研究中一个著名的结论是:当缺货需求不能被观测到时,最优贝叶斯库存水平总会高于短视策略库存水平,原因是决策者需要通过多订货来获取对需求分布的认识.这是基于风险中性的研究,然后现实中决策者都期望规避风险.基于贝叶斯信息更新研究了风险规避背景下需求部分可观测的多周期报童问题,决策者的周期内效用函数满足独立可加性公理.通过引入非正规化概率,研究发现,对风险规避的决策者,当其效用函数具有不变绝对风险规避特征时,最优贝叶斯库存水平也会高于短视策略库存水平.非正规化概率简化了动态规划方程与结果的证明.

A well-known result in the Bayesian inventory management research is： if lost sales are not observed, the Bayesian optimal inventory level is larger than the myopic inventory level. The underlying reason behind the fact is that the decision maker needs to stock more to learn about the demand distribution. These researches are based on the assumption that the decision maker is risk neutral. However, in reality, different decision makers often have different degree of risk aversion. In this paper, a multi-period newsvendor problem with risk aversion and partially observed demand is considered. The decision maker uses the Bayesian rule to update the information of the demand distribution, and the utility is characterized by the sum of the intraperiod utility functions which satisfy the additive independence axiom. Our research, by using the interesting concept of unnormalized probability, shows that as the decision maker is risk averse and the utility function is the negative exponential function with a constant coefficient of absolute risk aversion, the Bayesian optimal inventory level is also larger than the myopic inventory level. The unnormalized probability greatly simplifies the dynamic programming equation and facilitates the technical proof of the result.