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Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Revised version of F-409)

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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

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple (Y,Z, ψ) where Y is a semimartingale, and (Z, ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of Y ’s future paths, as well as quadratic and exponential growth on the spot values of (Z, ψ), respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on (Z, ψ) with respect to the forward process are also obtained.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2018. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Revised version of F-409)," CARF F-Series CARF-F-431, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf431
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    References listed on IDEAS

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    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. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    3. Olivier Menoukeu Pamen, 2015. "Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 998-1031, December.
    4. 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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