Reflected BSDEs Driven by Lévy Processes and Countable Brownian Motions

Jean-Marc Owo

UFR de Mathématiques et Informatique, Université Félix H. Boigny, Abidjan, Côte d’Ivoire.

DOI: 10.4236/am.2015.614197                

Abstract

A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the existence and uniqueness of solution to this kind of RBSDEs are obtained.

Keywords

Backward Doubly Stochastic Differential Equations, Lévy Processes, Teugels Martingales, Countable Brownian Motions

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ren, Y. (2010) Reflected Backward Doubly Stochastic Differential Equations Driven by a Lévy Process. C. R. Acad. Sci. Paris, Ser. I, 348, 439-444.
[2]	Yan, J., He, S. and Wang, J. (1995) Semimartingale and Stochastic Analysis. Scientific Press, Beijing,
[3]	Duan, P.J., Ren, M. and Fei, S.L. (2013) Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions. Journal of Applied Mathematics, 2013, Article ID: 729636.
[4]	Owo, J.-M. (2015) Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions with Continuous Coefficients. Electronic Communications in Probability, 20, 1-11. http://dx.doi.org/10.1214/ECP.v20-3771
[5]	Nualart, D. and Schoutens, W. (2001) Backward Stochastic Differential Equations and Feynman-Kac Formula for Lévy Processes with Applications in Finance. Bernoulli, 7, 761-776. http://dx.doi.org/10.2307/3318541
[6]	Saisho, Y. (1987) SDE for Multidimensional Domains with Reflecting Boundary. Probability Theory and Related Fields, 74, 455-477. http://dx.doi.org/10.1007/BF00699100