2014•arXiv (Cornell University)Open access

Optimal stopping for dynamic risk measures with jumps and obstacle problems

Roxana Dumitrescu, Marie-Claire Quenez, Agnès Sulem

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.

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Key concepts: Variational inequality, Obstacle, Obstacle problem, Optimal stopping, Viscosity solution, Uniqueness, Dynamic risk measure, Bellman equation