Path regularity and explicit convergence rate for BSDE with truncated quadratic growth

Details Path regularity and explicit convergence rate for BSDE with truncated quadratic growth Path regularity and explicit convergence rate for BSDE with truncated quadratic growth

2009-05-06

arxiv.org/abs/0905.0788v3

Stochastic Processes and Their Applications, 2010, 120, 348-379

Mathematics

Probability

30 pages

Scientific paper

10.1016/j.spa.2009.11.004

We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the solution processes of the qgBSDE, in particular we prove an extension of Zhang's path regularity theorem to the quadratic growth setting. We give explicit convergence rates for the difference between the solution of a qgBSDE and its truncation, filling an important gap in numerics for qgBSDE. We give an alternative proof of second order Malliavin differentiability for BSDE with drivers that are Lipschitz continuous (and differentiable), and then derive an analogous result for qgBSDE.

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