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Backward stochastic differential equations associated to jump Markov processes and applications

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  • Confortola, Fulvia
  • Fuhrman, Marco

Abstract

In this paper we study backward stochastic differential equations (BSDEs) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space K. We apply these results to prove well-posedness of a class of nonlinear parabolic differential equations on K, that generalize the Kolmogorov equation of X. Finally we formulate and solve optimal control problems for Markov jump processes, relating the value function and the optimal control law to an appropriate BSDE that also allows to construct probabilistically the unique solution to the Hamilton–Jacobi–Bellman equation and to identify it with the value function.

Suggested Citation

  • Confortola, Fulvia & Fuhrman, Marco, 2014. "Backward stochastic differential equations associated to jump Markov processes and applications," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 289-316.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:289-316
    DOI: 10.1016/j.spa.2013.07.010
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    References listed on IDEAS

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    1. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions," Papers 0810.0055, arXiv.org, revised Jan 2010.
    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.
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    Cited by:

    1. Qingda Wei, 2016. "Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 461-487, December.
    2. Bandini, Elena & Fuhrman, Marco, 2017. "Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1441-1474.
    3. Dirk Becherer & Martin Buttner & Klebert Kentia, 2016. "On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples," Papers 1607.06644, arXiv.org, revised Nov 2019.

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