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On backward stochastic differential equations and strict local martingales

Xing, Hao (2012) On backward stochastic differential equations and strict local martingales. Stochastic Processes and Their Applications, 122 (6). pp. 2265-2291. ISSN 0304-4149

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Abstract

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 Lp 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.

Item Type: Article
Official URL: http://www.journals.elsevier.com/stochastic-proces...
Additional Information: © 2012 Elsevier
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 May 2012 09:40
URL: http://eprints.lse.ac.uk/43459/

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