Stochastic Comparative Statics in Markov Decision Processes

• 成果类型: Article
• 署名作者: Light, Bar
• 署名单位: Stanford University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1086
• 发表日期: 2021
• 页码: 797-810
• 关键词: dynamics; RISK; equilibrium; economies; STABILITY; games

摘要

In multiperiod stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. I analyze how the expected value of this random variable changes as a function of the dynamic optimization parameters in the context of Markov decision processes. I call this analysis stochastic comparative statics. I derive both comparative statics results and stochastic comparative statics results showing how the current and future optimal decisions change in response to changes in the single-period payoff function, the discount factor, the initial state of the system, and the transition probability function. I apply my results to various models from the economics and operations research literature, including investment theory, dynamic pricing models, controlled random walks, and comparisons of stationary distributions.