## Bernoulli

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

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

#### 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.

#### Article information

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

Dates
Revised: March 2014
First available in Project Euclid: 30 September 2015

https://projecteuclid.org/euclid.bj/1443620859

Digital Object Identifier
doi:10.3150/14-BEJ667

Mathematical Reviews number (MathSciNet)
MR3449792

Zentralblatt MATH identifier
1339.60094

#### Citation

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. https://projecteuclid.org/euclid.bj/1443620859

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