Home Lp -solution for BSDEs driven by a Lévy process
Article
Licensed
Unlicensed Requires Authentication

Lp -solution for BSDEs driven by a Lévy process

  • Mohamed El Jamali EMAIL logo
Published/Copyright: February 28, 2023

Abstract

This paper deals with the problem of existence and uniqueness of 𝕃 p -solutions for a backward stochastic differential equation in a filtration that supports Lévy processes with p ( 1 , 2 ) . However, we will focus on when the data satisfy the appropriate integrability conditions and when the coefficient is Lipschitz.


Communicated by Anatoly F. Turbin


References

[1] K. Bahlali, M. Eddahbi and E. Essaky, BSDE associated with Lévy processes and application to PDIE, J. Appl. Math. Stoch. Anal. 16 (2003), no. 1, 1–17. 10.1155/S1048953303000017Search in Google Scholar

[2] J. Bertoin, Lévy Processes, Cambridge Tracts in Math. 121, Cambridge University, Cambridge, 1996. Search in Google Scholar

[3] P. 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. 10.1016/S0304-4149(03)00089-9Search in Google Scholar

[4] S. Chen, L p solutions of one-dimensional backward stochastic differential equations with continuous coefficients, Stoch. Anal. Appl. 28 (2010), no. 5, 820–841. 10.1080/07362994.2010.503456Search in Google Scholar

[5] N. El Karoui, S. Peng and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997), no. 1, 1–71. 10.1111/1467-9965.00022Search in Google Scholar

[6] M. El Otmani, Backward stochastic differential equations associated with Lévy processes and partial integro-differential equations, Commun. Stoch. Anal. 2 (2008), no. 2, 277–288. 10.31390/cosa.2.2.07Search in Google Scholar

[7] M. E. Jamali and M. El Otmani, Predictable representation for time inhomogeneous Lévy processes and BSDEs, Afr. Mat. 30 (2019), no. 5–6, 697–714. 10.1007/s13370-019-00677-0Search in Google Scholar

[8] 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. 10.1080/17442508.2015.1090990Search in Google Scholar

[9] T. Kruse and A. Popier, L p -solution for BSDEs with jumps in the case p & l t ; 2 : Corrections to the paper BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration [MR3473849], Stochastics 89 (2017), no. 8, 1201–1227. 10.1080/17442508.2017.1290095Search in Google Scholar

[10] D. Nualart and W. Schoutens, Backward stochastic differential equations and Feynman–Kac formula for Lévy processes, with applications in finance, Bernoulli 7 (2001), no. 5, 761–776. 10.2307/3318541Search in Google Scholar

[11] E. Pardoux and S. Peng, Adapted solution of backward stochastic differential equations, Systems Control Lett. 14 (1990), 51–61. 10.1016/0167-6911(90)90082-6Search in Google Scholar

[12] P. E. Protter, Stochastic Integration and Differential Equations, 2nd ed., Appl. Math. (New York) 21, Springer, Berlin, 2005. 10.1007/978-3-662-10061-5_6Search in Google Scholar

[13] K.-I. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Stud. Adv. Math. 68, Cambridge University, Cambridge, 1999. Search in Google Scholar

[14] S. Yao, 𝕃 p solutions of backward stochastic differential equations with jumps, Stochastic Process. Appl. 127 (2017), no. 11,3465–3511. 10.1016/j.spa.2017.03.005Search in Google Scholar

Received: 2021-10-02
Accepted: 2022-04-15
Published Online: 2023-02-28
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 30.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/rose-2023-2006/html
Scroll to top button