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

  • Fulvia ConfortolaEmail author
Original Article
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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.

Keywords

Backward stochastic differential equations Marked point processes Stochastic optimal control 

Mathematics Subject Classification

60H10 60G55 93E20 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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