• Bernoulli
  • Volume 22, Number 1 (2016), 530-562.

Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression

Emmanuel Gobet and Plamen Turkedjiev

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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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Bernoulli, Volume 22, Number 1 (2016), 530-562.

Received: August 2013
Revised: March 2014
First available in Project Euclid: 30 September 2015

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backward stochastic differential equations dynamic programming equation empirical regressions Malliavin calculus non-asymptotic error estimates


Gobet, Emmanuel; Turkedjiev, Plamen. Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression. Bernoulli 22 (2016), no. 1, 530--562. doi:10.3150/14-BEJ667.

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