Optimal stopping for dynamic risk measures with jumps and obstacle problems

TL;DR

This paper investigates optimal stopping problems for dynamic risk measures driven by BSDEs with jumps, demonstrating that the value function solves a viscosity solution of an obstacle problem for a partial integro-differential variational inequality, with uniqueness established.

Contribution

It introduces a novel connection between dynamic risk measures with jumps and obstacle problems for integro-differential variational inequalities, including a uniqueness result.

Findings

Value function characterized as viscosity solution

Established uniqueness of the solution

Extended the theory to jump-diffusion settings

Abstract

We study the optimal stopping problem for a monotonous dynamic risk measure induced by a BSDE with jumps in the Markovian case. We show that the value function is a viscosity solution of an obstacle problem for a partial integro-differential variational inequality, and we provide an uniqueness result for this obstacle problem.