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Existence of the solutions of backward-forward SDE's with continuous monotone coefficients

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  • Antonelli, Fabio
  • Hamadène, SaI¨d

Abstract

We seek an alternative approach to produce the solution of a certain class of BFSDE's without employing the classical time restriction. In the literature there are various results about this problem, none of them implying the other. The previous methods always assume to have globally Lipschitz coefficients. Here, under some particular choices for the coefficients, we show that if one of them satisfies a uniform growth condition and they are accordingly monotone, one can find a solution (not necessarily unique), without even resorting to the Lipschitz property. Finally we provide some examples to show this is a new class of equations.

Suggested Citation

  • Antonelli, Fabio & Hamadène, SaI¨d, 2006. "Existence of the solutions of backward-forward SDE's with continuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1559-1569, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1559-1569
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    References listed on IDEAS

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    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. 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.
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    Cited by:

    1. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamaï, 2021. "Equilibrium asset pricing with transaction costs," Finance and Stochastics, Springer, vol. 25(2), pages 231-275, April.
    2. Huang, Zongyuan & Lepeltier, Jean-Pierre & Wu, Zhen, 2010. "Reflected forward-backward stochastic differential equations with continuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1569-1576, November.
    3. Luo, Peng & Menoukeu-Pamen, Olivier & Tangpi, Ludovic, 2022. "Strong solutions of forward–backward stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 1-22.

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