On backward stochastic differential equations and strict local martingales

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Xing, Hao

关键词: Backward stochastic differential equation;    Strict local martingale;    Viscosity solution;    Comparison theorem;   

DOI  :  10.1016/j.spa.2012.03.003

来源: Elsevier

【 摘 要 】

We study a backward stochastic differential equation (BSDE) whose terminal condition is an integrable function of a local martingale and generator has bounded growth in z. When the local martingale is a strict local martingale, the BSDE admits at least two different solutions. Other than a solution whose first component is of class D, there exists another solution whose first component is not of class D and strictly dominates the class D solution. Both solutions are L-p integrable for any 0 < p < 1. These two different BSDE solutions generate different viscosity solutions to the associated quasi-linear partial differential equation. On the contrary, when a Lyapunov function exists, the local martingale is a martingale and the quasi-linear equation admits a unique viscosity solution of at most linear growth. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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