Risk-sensitive control of branching processes

Abstract

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 IIE Transactions, datasets, additional tables, detailed proofs, etc.