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Article Dans Une Revue Stochastic Processes and their Applications Année : 2013

Second order backward stochastic differential equations with quadratic growth

Chao Zhou
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Résumé

We extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012) [31] to the case of a bounded terminal condition and a generator with quadratic growth in the z variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman-Kac formula and a probabilistic representation for fully non-linear PDEs in this setting.

Dates et versions

hal-00919127 , version 1 (16-12-2013)

Identifiants

Citer

Dylan Possamaï, Chao Zhou. Second order backward stochastic differential equations with quadratic growth. Stochastic Processes and their Applications, 2013, 123 (10), pp.3770-3799. ⟨10.1016/j.spa.2013.05.007⟩. ⟨hal-00919127⟩
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