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Journal Articles Stochastic Processes and their Applications Year : 2014

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

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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.

Dates and versions

hal-00773708 , version 1 (14-01-2013)

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Marie-Claire Quenez, Agnès Sulem. Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps. Stochastic Processes and their Applications, 2014, Stochastic Processes and their Applications, 124 (9), pp.23. ⟨hal-00773708⟩
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