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A Bismut–Elworthy formula for quadratic BSDEs

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  • Masiero, Federica

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.

Suggested Citation

  • Masiero, Federica, 2015. "A Bismut–Elworthy formula for quadratic BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1945-1979.
  • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1945-1979
    DOI: 10.1016/j.spa.2014.12.003
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    References listed on IDEAS

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    1. Briand, Philippe & Confortola, Fulvia, 2008. "BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 818-838, May.
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    1. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

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