Skip to main content
Log in

On Comparison Theorem and Solutions of BSDEs for Lévy Processes

  • Original Papers
  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we consider backward stochastic differential equations driven by a Lévy process. A comparison theorem and an existence and uniqueness theorem of BSDEs with non-Lipschitz coefficients are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bertoin, J. Lévy processes. Cambridge University Press, Cambridge, London, 1996

  2. He, S., Wang, J., Yan, J. Semimartingal theory and stochastic calculus. Science Press and CRC Press, Inc. 1992

  3. León, J.A., Solé, J.L., Utzet, F., Vives, J. On Lévy processes, Malliavin calculus and market models with jumps. Finance and Stochastics , 6:197–225 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lin, Q. Nonlinear Doob-Meyer Decomposition with jumps. Acta Mathematica Sinica, English Series, 19(1):69–78 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Mao, X. Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients. Stochastic Process. Appl., 58:281–292 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Nualart, D., Schoutens, W. Chaotic and predictable representations for Lévy processes. Stochastic Process. Appl., 90:109–122 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nualart, D., Schoutens, W. Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance. Bernoulli, 7(5):761–776 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ouknine, Y. Reflected backward stochastic differential equations with jumps. Stochastic Stochastic Rep., 65:111–125 (1998)

    MATH  MathSciNet  Google Scholar 

  9. Pardoux, E., Peng, S. Adapted solutions of a backward stochastic differential equation. Systems Control Letter., 14:55–61 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sato, K. Lévy processes and Infinitely Divisible Distributions. Cambridge Stud. Ade. Math., Vol. 68. Cambridge:Cambridge University Press, 1999

  11. Situ, R. On solutions of backward stochastic differential equations with jumps and application. Stochastic Process. Appl., 66:209–236 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qing Zhou.

Additional information

Supported by the National Natural Science Foundation of China (No. 10671205).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, Q. On Comparison Theorem and Solutions of BSDEs for Lévy Processes. Acta Mathematicae Applicatae Sinica, English Series 23, 513–522 (2007). https://doi.org/10.1007/s10255-007-0391-2

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-007-0391-2

Keywords

2000 MR Subject Classification

Navigation