A Bismut–Elworthy formula for quadratic BSDEs

Federica Masiero

Stochastic Processes and their Applications, 2015, vol. 125, issue 5, 1945-1979

Abstract: 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 ∇v and final condition only bounded and continuous are given, as well as applications to stochastic optimal control problems with quadratic growth.

Keywords: Bismut formula; Quadratic backward stochastic differential equations; HJB equations with quadratic hamiltonian; Infinite dimensions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2014.12.003

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