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BSDEs with random default time and their applications to default risk

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  • Shige Peng
  • Xiaoming Xu

Abstract

In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions and a comparison theorem for their solutions. As an application, we get a saddle-point strategy for the related zero-sum stochastic differential game problem.

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  • Shige Peng & Xiaoming Xu, 2009. "BSDEs with random default time and their applications to default risk," Papers 0910.2091, arXiv.org.
    • Handle: RePEc:arx:papers:0910.2091
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    Cited by:

    1. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    2. Jingnan Wang & Ralf Korn, 2020. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk," Risks, MDPI, vol. 8(3), pages 1-30, July.
    3. Tomasz R. Bielecki & Igor Cialenco & Marek Rutkowski, 2017. "Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models," Papers 1701.08399, arXiv.org, revised Apr 2018.

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