| Título: | Classical and Variational Differentiability of BSDEs with Quadratic Growth |
| Autores: |
Ankirchner, Stefan; Humboldt Uiversitaet Berlin Imkeller, Peter; Humboldt Uiversitaet Berlin Dos Reis, Goncalo JN; Humboldt Uiversitaet Berlin |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
BSDE, forward-backward SDE, quadratic growth, differentiability, stochastic calculus of variations, Malliavin calculus, Feynman-Kac formula, BMO martingale, reverse Holder inequality 2000 AMS subject classifications: Primary: 60H10; Secondary: 60H07, 65C30 |
| Descripción: | We consider Backward Stochastic Differential Equations (BSDEs) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector parameter $x$. We give sufficient conditions for the solution pair of the BSDE to be differentiable in $x$. These results can be applied to systems of forward-backward SDE. If the terminal condition of the BSDE is given by a sufficiently smooth function of the terminal value of a forward SDE, then its solution pair is differentiable with respect to the initial vector of the forward equation. Finally we prove sufficient conditions for solutions of quadratic BSDEs to be differentiable in the variational sense (Malliavin differentiable). |
| Idioma: | No aplica |
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