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Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems

Author

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  • Roxana Dumitrescu

    (Université Paris 9 Dauphine
    CREST and INRIA Paris-Rocquencourt)

  • Marie-Claire Quenez

    (Université Paris 7 Denis Diderot)

  • Agnès Sulem

    (INRIA Paris-Rocquencourt
    Université Paris-Est)

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.

Suggested Citation

  • Roxana Dumitrescu & Marie-Claire Quenez & Agnès Sulem, 2015. "Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 219-242, October.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0635-2
    DOI: 10.1007/s10957-014-0635-2
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    References listed on IDEAS

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    1. Quenez, Marie-Claire & Sulem, Agnès, 2013. "BSDEs with jumps, optimization and applications to dynamic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3328-3357.
    2. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    3. Quenez, Marie-Claire & Sulem, Agnès, 2014. "Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3031-3054.
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    Cited by:

    1. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2017. "American options in an imperfect market with default," Papers 1708.08675, arXiv.org.
    2. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.

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