Optimal stopping for dynamic risk measures with jumps and obstacle problems

Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès

Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès (2015), Optimal stopping for dynamic risk measures with jumps and obstacle problems, Journal of Optimization Theory and Applications, 167, 1, p. 219-242. http://dx.doi.org/10.1007/s10957-014-0635-2

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1404.4600v2

Date

2015

Journal name

Journal of Optimization Theory and Applications

Volume

167

Number

Publisher

Plenum

Pages

219-242

Abstract (EN)

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.

Subjects / Keywords

partial integro-differential variational inequality; Dynamic risk-measure; obstacle problem; optimal stopping; reflected backward stochastic differential equations with jumps; comparison principle