Stochastic Comparative Statics in Markov Decision Processes

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.

Automated summary

In the context of multiperiod stochastic optimization problems, the analysis of how the expected value of future optimal decisions changes with dynamic optimization parameters is referred to as stochastic comparative statics. The study presents results on how both current and future optimal decisions respond to changes in the single-period payoff function, discount factor, initial state of the system, and transition probability function, applied to various models in economics and operations research.