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 decisions are insensitive (robust) to the precise assignment of prior probabilities. This holds independent from whether the preference for robustness is global or restricted to local perturbations around some reference model.