Reflected Backward Stochastic Differential Equations Associated to Jump Markov Processes and Application to Partial Differential Equations

Abdelkarim Oualaid (), Khaled Bahlali () and Youssef Ouknine ()
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Abdelkarim Oualaid: LIBMA, Cadi Ayyad University
Khaled Bahlali: Toulon University, IMATH
Youssef Ouknine: LIBMA, Cadi Ayyad University

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1400-1436

Abstract: Abstract In this paper, we study a class of reflected backward stochastic differential equations (RBSDEs) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space U. The reflection keeps the solution above a given càdlàg process. We prove the uniqueness and existence both by a combination of the Snell envelope theory and a fixed-point argument. As a consequence of these results, the Markovian structure of X allows us to represent probabilistically the solution of some quasi-variational inequalities problem.

Keywords: Backward stochastic differential equations; Jump Markov processes; Marked point processes; Quasi-variational inequalities; 60J76; 60H10; 60G57; 35A23 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01212-x

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