On the Relation between Robust and Bayesian Decision Making

This paper compares Bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization. For a class of robust decision problems there exists a sequence of Bayesian decision problems whose solution converges towards the robust solution. It is shown that the limiting Bayesian problem displays infinite risk aversion and that its solution is insensitive (robust) to the precise assignment of prior probabilities. Moreover, the limiting Bayesian objective turns out not to be time separable even if the objective function of the robust decision makers displays time separability.