Second Order Backward Stochastic Differential Equations with Quadratic Growth

Details Second Order Backward Stochastic Differential Equations with Quadratic Growth Second Order Backward Stochastic Differential Equations with Quadratic Growth

2012-01-03

arxiv.org/abs/1201.1050v2

Mathematics

Probability

27 pages

Scientific paper

We prove the existence and uniqueness of a solution for one-dimensionnal
second order backward stochastic differential equations introduced by Soner,
Touzi and Zhang (2010), with a bounded terminal condition and a generator which
is continuous with quadratic growth in z. We also prove a Feyman-Kac formula
and a probabilistic representation for fully nonlinear PDEs in this setting.

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