BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces

Abstract

This paper is devoted to the study of the differentiability of solutions to real-valued backward stochastic differential equations (BSDEs for short) with quadratic generators driven by a cylindrical Wiener process. The main novelty of this problem consists in the fact that the gradient equation of a quadratic BSDE has generators which satisfy stochastic Lipschitz conditions involving BMO martingales. We show some applications to the nonlinear Kolmogorov equations.

References in corpus (3)

• Utility maximization in incomplete markets
• BSDE with quadratic growth and unbounded terminal value
• Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

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