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

By Peter Imkeller, Gonçalo dos Reis. 2009

80 citations recorded by the source corpus.

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.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/97e370262cca1904598862e696376f723b669f88

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Citations in the corpus

• Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, unknown): “When κ = 1, it is also possible to recover the result obtained by Imkeller and dos Reis in [18] (they assume in addition that r = 0): for all k ∈ N, there exists C > 0 such that ē1(M) 6 C Mk .”
• Numerical simulation of BSDEs with drivers of quadratic growth (2010, methodology): “For their original version and their proof we refer to [2, 17] and [14].”
• Numerical simulation of quadratic BSDEs (2013, unknown): “The error is bounded by C p M p for every p > 1; see [28, 40].”
• Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2011, methodology): “Again in this forward– backward setting, if the generator f has a quadratic growth in Z, a numerical approximation is developed by Imkeller and Dos Reis [9] in which a truncation procedure is applied.”