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- W2000492429 abstract "Abstract We show existence and uniqueness of solutions to BSDEs of the form Y t = ξ + ∫ t T f ( s , Y s , Z s ) d s − ∫ t T Z s d W s in the case where the terminal condition ξ has bounded Malliavin derivative. The driver f ( s , y , z ) is assumed to be Lipschitz continuous in y but only locally Lipschitz continuous in z. In particular, it can grow arbitrarily fast in z. If in addition to having bounded Malliavin derivative, ξ is bounded, the driver needs only be locally Lipschitz continuous in y. In the special case where the BSDE is Markovian, we obtain existence and uniqueness results for semilinear parabolic PDEs with non-Lipschitz nonlinearities. We discuss the case where there is no lateral boundary as well as lateral boundary conditions of Dirichlet and Neumann type." @default.
- W2000492429 created "2016-06-24" @default.
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- W2000492429 date "2014-02-01" @default.
- W2000492429 modified "2023-09-28" @default.
- W2000492429 title "BSDEs with terminal conditions that have bounded Malliavin derivative" @default.
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- W2000492429 doi "https://doi.org/10.1016/j.jfa.2013.12.004" @default.
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