  In multi-period stochastic optimization problems, the future optimal decision
is a random variable whose distribution depends on the parameters of the
optimization problem. We 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. We call this analysis \emph{stochastic comparative
statics}. We derive both \emph{comparative statics} results and
\emph{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. We apply our 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.
