BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATIONS

Résumé

We are first interested on viscosity solutions of parabolic Partial Differential Equations through Reflected BSDEs where the existence and uniqueness of viscosity solutions for a class of system of differential integro-partial equations through the RBSDEs with jumps at one barrier. Next we are interested in other classes of BSDEs, in particular by generalizing the work of Delong, L. and Imkeller, P. [22], by adopting the fractional Brownian motion with the Hurst parameter greater than 1/2 to establish the existence and uniqueness of solutions for a sufficiently small time horizon or for a sufficiently small Lipschitz con- stant of a generator using the divergence operator of integral type. Subsequently, we focus on generalized anticipated BSDEs, where under Mao’s con- ditions, the existence and uniqueness of solutions of this family of BSDEs are proven, in extension of the work of Wu and all [76], who proved the existence and uniqueness of solutions under Lipschitz conditions. The latest work is based on a class of generalized BSDEs driven by two mutually independent fractional Brownian motions where we show the existence and uniqueness of solutions for this family of BSDEs where in passing the link between the solution of this class of BSDEs and that of Partial Differential Equations (PDE) is established.

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