English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A novel discretization is presented for forward-backward stochasticdifferential equations (FBSDE) with differentiable coefficients, simultaneouslysolving the BSDE and its Malliavin sensitivity problem. The control process isestimated by the corresponding linear BSDE driving the trajectories of theMalliavin derivatives of the solution pair, which implies the need to provideaccurate $\Gamma$ estimates. The approximation is based on a merged formulationgiven by the Feynman-Kac formulae and the Malliavin chain rule. The continuoustime dynamics is discretized with a theta-scheme. In order to allow for anefficient numerical solution of the arising semi-discrete conditionalexpectations in possibly high-dimensions, it is fundamental that the chosenapproach admits to differentiable estimates. Two fully-implementable schemesare considered: the BCOS method as a reference in the one-dimensional frameworkand neural network Monte Carlo regressions in case of high-dimensionalproblems, similarly to the recently emerging class of Deep BSDE methods [Han etal. (2018), Hur\'e et al. (2020)]. An error analysis is carried out to show$L^2$ convergence of order $1/2$, under standard Lipschitz assumptions andadditive noise in the forward diffusion. Numerical experiments are provided fora range of different semi- and quasi-linear equations up to $50$ dimensions,demonstrating that the proposed scheme yields a significant improvement in thecontrol estimations.

The One Step Malliavin scheme: new discretization of BSDEs implemented with deep learning regressions