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
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.
|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|
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