Discounted dynamic programming with unbounded returns: Application to economic models

作     者：Jaskiewicz, Anna Nowak, Andrzej S. 

作者机构：Wroclaw Univ Technol Inst Math & Comp Sci PL-50370 Wroclaw Poland Univ Zielona Gora Fac Math Comp Sci & Econometr PL-65246 Zielona Gora Poland 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (数学分析与应用杂志)

年 卷 期：2011年第378卷第2期

页      面：450-462页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Stochastic dynamic programming Bellman equation Stochastic optimal growth 

摘      要：In this paper, we study discounted Markov decision processes on an uncountable state space. We allow a utility (reward) function to be unbounded both from above and below. A new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function. This assumption, in turn, enables us to prove the convergence of a value iteration algorithm to a solution to the Bellman equation. Moreover, by virtue of the optimality equation we show the existence of an optimal stationary policy. (C) 2010 Elsevier Inc. All rights reserved.