Robust Utility in Contiuous Time

We study a general class of utility processes V(c)=(V_{t}(c)), where V_{t}(c), a dynamic utility operator, is a decision criterion that quantifies a decision maker's evaluation of uncertain consumption streams c. We call this dynamic utility operator robust and its distinctiveness is that it features the diffusion of the process V(c), i.e., the utility is affected by its own variability. A main result of this paper is to identify a general class of robust dynamic utility operators that are monotone and, yet, irreducibly depend on the utility variability. A principal motivation for studying such robust dynamic operators is that, by incorporating utility variability into the decision criterion, they bring a facility required to adapt models of ambiguity sensitive preferences to Brownian environments. In particular, those preference models which permit flexibility in ambiguity attitudes. We demonstrate this facility by obtaining continuous-time extensions of two prominent ambiguity aversion frameworks which incorporate variable ambiguity attitude, the smooth ambiguity model and the α-maxmin expected utility