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\(L^p\) solution of backward stochastic differential equations driven by a marked point process

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Abstract

We obtain existence and uniqueness in \(L^p\), \(p>1\) of the solutions of a backward stochastic differential equation (BSDE for short) driven by a marked point process, on a bounded interval. We show that the solution of the BSDE can be approximated by a finite system of deterministic differential equations. As application, we address an optimal control problem for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function.

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Acknowledgements

We wish to thank Prof. Jean Jacod for discussions on connections between BSDEs and point processes.

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  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Fulvia Confortola

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  1. Fulvia Confortola
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Correspondence to Fulvia Confortola.

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Confortola, F. \(L^p\) solution of backward stochastic differential equations driven by a marked point process. Math. Control Signals Syst. 31, 1 (2019). https://doi.org/10.1007/s00498-018-0230-4

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