Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps

2012/12/30 by Quenez, Marie-Claire, Agnès Sulem, Sulem, AgnÈs · 5 citations
Economics, Econometrics and Finance · Decision Sciences · Engineering · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Stability and Control of Uncertain Systems

paper · doi:10.48550/arxiv.1212.6744

Abstract

We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). We first provide general existence, uniqueness and comparison theorems for RBSDEs with jumps in the case of a RCLL adapted obstacle. We then show that the value function of the optimal stopping problem is characterized as the solution of an RBSDE. The existence of an optimal stopping time is obtained when the obstacle is left-upper semi-continuous along stopping times. Finally, robust optimal stopping problems related to the case with model ambiguity are investigated.

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