Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

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 inequalit...

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Veröffentlicht in:Journal of optimization theory and applications 2015-10, Vol.167 (1), p.219-242
Hauptverfasser: Dumitrescu, Roxana, Quenez, Marie-Claire, Sulem, Agnès
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Brownian motion
Calculus of Variations and Optimal Control
Optimization
Differential equations
Dynamic tests
Dynamics
Engineering
Inequalities
Mathematical models
Mathematics
Mathematics and Statistics
Obstacles
Operations Research/Decision Theory
Optimization
Random variables
Risk
Risk assessment
Studies
Theory of Computation
Uniqueness
Viscosity
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Beschreibung
Zusammenfassung: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-014-0635-2