A Bismut-Elworthy formula for quadratic BSDEs

作者：Masiero Federica^*

来源：Stochastic Processes and Their Applications, 2015, 125(5): 1945-1979.

DOI：10.1016/j.spa.2014.12.003

• Bismut formula
• Quadratic backward stochastic differential equations
• HJB equations with quadratic hamiltonian
• Infinite dimensions

We consider a backward stochastic differential equation in a Markovian framework for the pair of processes (Y, Z), with generator with quadratic growth with respect to Z. Under non-degeneracy assumptions, we prove an analogue of the well-known Bismut-Elworthy formula when the generator has quadratic growth with respect to Z. Applications to the solution of a semilinear Kolmogorov equation for the unknown v with nonlinear term with quadratic growth with respect to del(v) and final condition only bounded and continuous are given, as well as applications to stochastic optimal control problems with quadratic growth.

• 出版日期2015-5