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Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients

Author

Listed:
  • Jean-Marc Owo

    (Université Félix Houphouet-Boigny)

  • Auguste Aman

    (Université Félix Houphouet-Boigny)

Abstract

This paper deals with generalized backward doubly stochastic differential equations driven by a Lévy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp. maximal) solutions.

Suggested Citation

  • Jean-Marc Owo & Auguste Aman, 2023. "Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2311-2338, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01270-9
    DOI: 10.1007/s10959-023-01270-9
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    References listed on IDEAS

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    1. Mohamed El Otmani, 2006. "Generalized BSDE driven by a Lévy process," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-25, October.
    2. Nualart, David & Schoutens, Wim, 2000. "Chaotic and predictable representations for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 109-122, November.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. V. Bally & A. Matoussi, 2001. "Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 14(1), pages 125-164, January.
    Full references (including those not matched with items on IDEAS)

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