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Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability (Forthcoming in Stochastic Processes and their Applications)(revised version of CARF-F-395)

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  • Masaaki Fujii

    (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)

Abstract

We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called Aг-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence occurs under more general (not necessarily monotone) sequence of drivers, which is then applied to give the sufficient conditions for the Malliavin’s differentiability.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2017. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability (Forthcoming in Stochastic Processes and their Applications)(revised version of CARF-F-395)," CARF F-Series CARF-F-420, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf420
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    References listed on IDEAS

    as
    1. Antonelli, Fabio & Mancini, Carlo, 2016. "Solutions of BSDE’s with jumps and quadratic/locally Lipschitz generator," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3124-3144.
    2. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, vol. 13(1), pages 121-150, January.
    3. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    4. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    5. Briand, Philippe & Confortola, Fulvia, 2008. "BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 818-838, May.
    6. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs," CARF F-Series CARF-F-372, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," CIRJE F-Series CIRJE-F-993, CIRJE, Faculty of Economics, University of Tokyo.
    8. Delong, Lukasz & Imkeller, Peter, 2010. "On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1748-1775, August.
    9. Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
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