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Lp estimates for fully coupled FBSDEs with jumps

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  • Li, Juan
  • Wei, Qingmeng

Abstract

In this paper we study some useful estimates, in particular, Lp estimates, for fully coupled forward–backward stochastic differential equations (FBSDEs) with jumps. These estimates are proved at one hand for fully coupled FBSDEs with jumps under the monotonicity assumption for arbitrary time intervals and on the other hand for such equations on small time intervals. Moreover, the well-posedness of this kind of equation is studied and regularity results are obtained.

Suggested Citation

  • Li, Juan & Wei, Qingmeng, 2014. "Lp estimates for fully coupled FBSDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1582-1611.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:4:p:1582-1611
    DOI: 10.1016/j.spa.2013.12.005
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    1. 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.
    2. Buckdahn, Rainer & Hu, Ying & Li, Juan, 2011. "Stochastic representation for solutions of Isaacs’ type integral–partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2715-2750.
    3. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
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    Cited by:

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    2. Masaaki Fujii & Akihiko Takahashi, 2021. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," CIRJE F-Series CIRJE-F-1180, CIRJE, Faculty of Economics, University of Tokyo.
    3. Shamarova, Evelina & Sá Pereira, Rui, 2020. "Forward–backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3865-3894.
    4. René Aid & Andrea Cosso & Huyên Pham, 2022. "Equilibrium price in intraday electricity markets," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 517-554, April.
    5. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.

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