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
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 |
| Uncontrolled Keywords: | backward stochastic differential equation, strict local martingale, viscosity solution, comparison theorem |
| Library of Congress subject classification: | H Social Sciences > HA Statistics |
| Sets: | Departments > Statistics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/43459/ |
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