Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

Roxana Dumitrescu; Marie Claire Quenez; Agnès Sulem

doi:10.1007/s10957-014-0635-2

Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

Roxana Dumitrescu
, Marie Claire Quenez
, Agnès Sulem

Research output: Contribution to journal › Article › peer-review

Abstract

We study the optimal stopping problem for a monotonous dynamic risk measure induced by a Backward Stochastic Differential Equation 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.

Original language	English
Pages (from-to)	219-242
Number of pages	24
Journal	Journal of Optimization Theory and Applications
Volume	167
Issue number	1
DOIs	https://doi.org/10.1007/s10957-014-0635-2
Publication status	Published - 14 Oct 2015

Keywords

Comparison principle
Dynamic risk measures
Optimal stopping
Partial integro-differential variational inequality
Reflected backward stochastic differential equations with jumps
Viscosity solution

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10.1007/s10957-014-0635-2

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title = "Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems",

abstract = "We study the optimal stopping problem for a monotonous dynamic risk measure induced by a Backward Stochastic Differential Equation 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.",

keywords = "Comparison principle, Dynamic risk measures, Optimal stopping, Partial integro-differential variational inequality, Reflected backward stochastic differential equations with jumps, Viscosity solution",

author = "Roxana Dumitrescu and Quenez, \{Marie Claire\} and Agn{\`e}s Sulem",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

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AU - Dumitrescu, Roxana

AU - Quenez, Marie Claire

AU - Sulem, Agnès

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N2 - We study the optimal stopping problem for a monotonous dynamic risk measure induced by a Backward Stochastic Differential Equation 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.

AB - We study the optimal stopping problem for a monotonous dynamic risk measure induced by a Backward Stochastic Differential Equation 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.

KW - Comparison principle

KW - Dynamic risk measures

KW - Optimal stopping

KW - Partial integro-differential variational inequality

KW - Reflected backward stochastic differential equations with jumps

KW - Viscosity solution

U2 - 10.1007/s10957-014-0635-2

DO - 10.1007/s10957-014-0635-2

M3 - Article

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VL - 167

SP - 219

EP - 242

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

Abstract

Keywords

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