AI 中文总结
研究具有CES聚合器的离散时间无限期马尔可夫决策过程，在温和条件下证明贝尔曼方程解的存在唯一性及库普曼斯方程有唯一解，表明贝尔曼方程最大值的可测选择器是最优平稳策略，方法还用于研究其他确定性等价情况。
AI 中文摘要
本文研究具有由经典CES聚合器定义的递归效用以及确定性等价算子为熵风险测度的负的离散时间无限期马尔可夫决策过程（动态规划模型）。在原始数据的温和条件下，我们证明了贝尔曼方程解的存在性和唯一性。此外，我们表明对于任何给定的平稳策略，库普曼斯方程有唯一解。这两个事实意味着贝尔曼方程中最大值的可测选择器是最优平稳策略。我们的证明方法被应用于研究其他确定性等价情况下贝尔曼方程的解，包括风险中性情况。
英文摘要
In this paper we investigate discrete-time infinite horizon Markov decision processes (dynamic programming models) with recursive utilities defined by the classical \emph{CES} aggregator and the certainty equivalent operator being the negative of the entropic risk measure. Under mild conditions on the primitive data we prove existence and uniqueness of a solution to the Bellman equation. Moreover, we show that for any given stationary policy, the Koopmans equation has a unique solution. These two facts imply that a measurable selector of maxima in the Bellman equation is an optimal stationary policy. The methods of our proofs are applied to study solutions to the Bellman equation for other certainty equivalents, including risk-neutral case.
