On backward stochastic differential equations and strict local martingales

Mathematics – Probability

Scientific paper

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Keywords: Backward stochastic differential equation, strict local martingale, viscosity solution, comparison theorem

Scientific paper

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

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