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- W2950410168 abstract "We study a backward stochastic differential equation 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 $mathbb{L}^p$ 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." @default.
- W2950410168 created "2019-06-27" @default.
- W2950410168 creator A5068974015 @default.
- W2950410168 date "2011-05-15" @default.
- W2950410168 modified "2023-10-18" @default.
- W2950410168 title "On backward stochastic differential equations and strict local martingales" @default.
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- W2950410168 doi "https://doi.org/10.48550/arxiv.1105.2973" @default.
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