Stochastic comparative statics in Markov decision processes

Bar Light*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)797-810
Number of pages14
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2021
Externally publishedYes


  • Comparative statics
  • Markov decision processes
  • Stochastic comparative statics


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