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February 2016 Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression
Emmanuel Gobet, Plamen Turkedjiev
Bernoulli 22(1): 530-562 (February 2016). DOI: 10.3150/14-BEJ667

Abstract

We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration by parts-representation of the $Z$-component by (Ann. Appl. Probab. 12 (2002) 1390–1418). When the sequence of conditional expectations is computed using empirical least-squares regressions, we establish, under general conditions, tight error bounds as the time-average of local regression errors only (up to logarithmic factors). We compute the algorithm complexity by a suitable optimization of the parameters, depending on the dimension and the smoothness of value functions, in the limit as the number of grid times goes to infinity. The estimates take into account the regularity of the terminal function.

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Emmanuel Gobet. Plamen Turkedjiev. "Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression." Bernoulli 22 (1) 530 - 562, February 2016. https://doi.org/10.3150/14-BEJ667

Information

Received: 1 August 2013; Revised: 1 March 2014; Published: February 2016
First available in Project Euclid: 30 September 2015

zbMATH: 1339.60094
MathSciNet: MR3449792
Digital Object Identifier: 10.3150/14-BEJ667

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

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Vol.22 • No. 1 • February 2016
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