Risk-sensitive control of branching processes

This article solves the risk-sensitive control problem for branching processes where the one-period progeny of an individual can take values from a finite set. The decision maker is assumed to maximize the expected risk-averse exponential utility (or to minimize the expected risk-averse exponential disutility) of the rewards earned in an infinite horizon. Individuals are assumed to produce progeny independently, and with the same probability mass function if they take the same action. This article characterizes the expected disutility of stationary policies, identifies necessary and sufficient conditions for the existence of a stationary optimal policy that assigns the same action to all individuals in all periods, and discusses computational methods to obtain such a policy. Supplementary materials are available for this article. See the publisher’s online edition of <i>IIE Transactions,</i> datasets, additional tables, detailed proofs, etc.

本文针对单代个体后代取值于有限集合的分支过程（branching processes），求解其风险敏感控制问题（risk-sensitive control problem）。本文假定决策者以最大化无限时域（infinite horizon）下累计回报的风险厌恶型指数效用（或最小化其风险厌恶型指数负效用）为目标。假定个体独立繁衍后代，且当不同个体采取相同行动时，其后代替从同一概率质量函数（probability mass function）。本文刻画了平稳策略（stationary policy）的期望负效用，推导了存在可在全时期为所有个体分配统一行动的平稳最优策略的充要条件，并探讨了获取该策略的计算方法。本文附带补充材料，可查阅出版商在线版《IIE Transactions》中的数据集、附加表格、详细证明等内容。