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On solutions of backward stochastic differential equations with jumps and applications

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  • Rong, Situ

Abstract

For backward stochastic differential equation (BSDE) with jumps and with non-Lipschitzian coefficient the existence and uniqueness of an adapted solution is obtained. By generalizing the existence result on partial differential and integral equations (PDIE) and Ito formula to the functions with only first and second Sobolev derivatives the probabilistic interpretation for solutions of PDIE (a new Feynman-Kac formula) by means of solutions of BSDE with jumps is got. With the help of this formula a new existence and uniqueness result for the solution of PDIE with non-Lipschitzian force is obtained. The convergence theorems of solutions to BSDE and PDIE are also derived.

Suggested Citation

  • Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:2:p:209-236
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    References listed on IDEAS

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    1. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
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    Cited by:

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    4. T. Sathiyaraj & T. Ambika & Ong Seng Huat, 2023. "Exponential Stability of Fractional Large-Scale Neutral Stochastic Delay Systems with Fractional Brownian Motion," JRFM, MDPI, vol. 16(5), pages 1-15, May.
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    6. N. C. Framstad & B. Øksendal & A. Sulem, 2004. "Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 77-98, April.
    7. Tu, Shuheng & Hao, Wu & Chen, Jing, 2017. "The adapted solutions and comparison theorem for anticipated backward stochastic differential equations with Poisson jumps under the weak conditions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 7-17.
    8. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2018. "Computing Credit Valuation Adjustment solving coupled PIDEs in the Bates model," Papers 1809.05328, arXiv.org.
    9. Sundar, P. & Yin, Hong, 2009. "Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1216-1234, April.
    10. Ramin Okhrati & Uwe Schmock, 2015. "It\^o's formula for finite variation L\'evy processes: The case of non-smooth functions," Papers 1507.00294, arXiv.org.

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