[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j210626

𝔻-SOLUTIONS OF BSDES WITH POISSON JUMPS

Hassairi, Imen (School of Mathematical Sciences Wenzhou-Kean University)

Publication Information

Journal of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1083-1101 More about this Journal

Abstract

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

Keywords

Backward SDEs; Poisson point process; Lipschitz generator; $\mathbb{L}^p$ -solution;

Citations & Related Records

Reference

1	S. Rong, On solutions of backward stochastic differential equations with jumps and applications, Stochastic Process. Appl. 66 (1997), no. 2, 209-236. https://doi.org/10.1016/S0304-4149(96)00120-2 DOI
2	P. E. Protter, Stochastic Integration and Differential Equations, second edition, Applications of Mathematics (New York), 21, Springer-Verlag, Berlin, 2004.
3	M.-C. Quenez and A. Sulem, BSDEs with jumps, optimization and applications to dynamic risk measures, Stochastic Process. Appl. 123 (2013), no. 8, 3328-3357. https://doi.org/10.1016/j.spa.2013.02.016 DOI
4	S. J. Tang and X. J. Li, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994), no. 5, 1447-1475. https://doi.org/10.1137/S0363012992233858 DOI
5	S. Yao, L^p solutions of backward stochastic differential equations with jumps, http://dx.doi.org/10.2139/ssrn.2806567 DOI
6	T. Kruse and A. Popier, BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 88 (2016), no. 4, 491-539. https://doi.org/10.1080/17442508.2015.1090990 DOI
7	Ph. Briand, B. Delyon, Y. Hu, E. Pardoux, and L. Stoica, L^p solutions of backward stochastic differential equations, Stochastic Process. Appl. 108 (2003), no. 1, 109-129. https://doi.org/10.1016/S0304-4149(03)00089-9 DOI
8	C. Dellacherie and P.-A. Meyer, Probabilit'es et potentiel V-VIII, Hermann, Paris, 1980.
9	E. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55-61. https://doi.org/10.1016/0167-6911(90)90082-6 DOI
10	E. Pardoux, Generalized discontinuous backward stochastic differential equations, in Backward stochastic differential equations (Paris, 1995-1996), 207-219, Pitman Res. Notes Math. Ser., 364, Longman, Harlow, 1997.