Skip to main content
Log in

Reflected Backward Stochastic Differential Equation with Jumps and Viscosity Solution of Second Order Integro-Differential Equation Without Monotonicity Condition: Case with the Measure of Lévy Infinite

Acta Mathematica Scientia Aims and scope Submit manuscript

Abstract

We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy’s measure is infinite.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barles G, Buckdahn R, Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stochastics: An International Journal of Probability and Stochastic Processes, 1997, 60: 57–83

    MathSciNet  MATH  Google Scholar 

  2. Fujiwara T, Kunita H. Stochastic differential equations of jump type and Lévy processes in differomorphism group. J Math Kyoto Univ, 1985, 25(1): 71–106

    Article  MathSciNet  MATH  Google Scholar 

  3. Hamadene S. Viscosity solutions of second order integral-partial differential equations without monotonicity condition: A new result. Nonlinear Analysis, 2016, 147: 213–235

    Article  MathSciNet  MATH  Google Scholar 

  4. Hamadène S, Morlais M -A. Viscosity solutions for second order integro-differential equations without monotonicity condition: The probabilistic Approach. Stochastics, 2016, 88(4): 632–649

    Article  MathSciNet  MATH  Google Scholar 

  5. Hamadène S, Ouknine Y. Reflected backward stochastic differential equation with jumps and random obstacle. Electron J Probab, 2003, 8(2): 1–20

    MathSciNet  MATH  Google Scholar 

  6. Harraj N, Ouknine Y, Turpin I. Double barriers Reflected BSDEs with jumps and viscosity solutions of parabolic Integro-differential PDEs. J Appl Math Stoch Anal, 2005, 1: 37–53

    Article  MATH  Google Scholar 

  7. Lenglart E, Lépingle D, Pratelli M. Présentation unifiée de certaines inégalités de la théorie des martingales. Séminaire de probabilités (Strasbourg), tome, 1980, 14: 26–48

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lamine Sylla.

Additional information

The author is supported by the CEAMITIC.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sylla, L. Reflected Backward Stochastic Differential Equation with Jumps and Viscosity Solution of Second Order Integro-Differential Equation Without Monotonicity Condition: Case with the Measure of Lévy Infinite. Acta Math Sci 39, 819–844 (2019). https://doi.org/10.1007/s10473-019-0312-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-019-0312-5

Key words

2010 MR Subject Classification

Navigation