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.

Masiero F. (2015). A Bismut-Elworthy formula for quadratic BSDEs. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 125(5), 1945-1979 [10.1016/j.spa.2014.12.003].

A Bismut-Elworthy formula for quadratic BSDEs

Masiero, F.
2015

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.
Articolo in rivista - Articolo scientifico
Bismut formula; HJB equations with quadratic hamiltonian; Infinite dimensions; Quadratic backward stochastic differential equations;
Bismut formula; HJB equations with quadratic hamiltonian; Infinite dimensions; Quadratic backward stochastic differential equations; Modeling and Simulation; Statistics and Probability; Applied Mathematics
English
1945
1979
35
Masiero F. (2015). A Bismut-Elworthy formula for quadratic BSDEs. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 125(5), 1945-1979 [10.1016/j.spa.2014.12.003].
Masiero, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99227
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