An ergodic BSDE risk representation in a jump-diffusion framework

Abstract

We consider the representation of forward entropic risk measures using the theory of ergodic backward stochastic differential equations in a jump-diffusion framework. Our paper can be viewed as an extension of the work considered by Chong et al in the diffusion case. We also study the behaviour of a forward entropic risk measure under jumps when a financial position is held for a longer maturity.