Stochastic Control of Optimized Certainty Equivalents

Optimized certainty equivalents (OCEs) are a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability the fact that it encompasses important examples, including entropic average value-at-risk. In this work we consider stochastic optimal control problems where objective criterion given an OCE measure or, in other words, minimization problem for controlled diffusions. A major difficulty arises since OCEs often time-inconsistent. Nevertheless, via enlargement state space achieve substitute sorts time-consistency fair generality. allows us derive dynamic programming principle thus recover central results (risk-neutral) theory. particular, show value our can be characterized as viscosity solution Hamilton--Jacobi--Bellman--Isaacs equation. We further establish comparison uniqueness latter under suitable technical conditions.