DeepAI AI Chat
Log In Sign Up

High-order combined Multi-step Scheme for solving forward Backward Stochastic Differential Equations

by   Long Teng, et al.

In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014), pp.A1731-A1751] by combining multi-steps. Two reference ordinary differential equations containing the conditional expectations and their derivatives are derived from the backward component. These derivatives are approximated by finite difference methods with multi-step combinations. The resulting scheme is a semi-discretization in the time direction involving conditional expectations, which are solved by using the Gaussian quadrature rules and polynomial interpolations on the spatial grids. Our new proposed multi-step scheme allows for higher convergence rate up to ninth order, and are more efficient. Finally, we provide a numerical illustration of the convergence of the proposed method.


page 1

page 2

page 3

page 4


Novel multi-step predictor-corrector schemes for backward stochastic differential equations

Novel multi-step predictor-corrector numerical schemes have been derived...

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

A novel discretization is presented for forward-backward stochastic diff...

Gradient boosting-based numerical methods for high-dimensional backward stochastic differential equations

In this work we propose a new algorithm for solving high-dimensional bac...

Numerical Methods for Backward Stochastic Differential Equations: A Survey

Backwards Stochastic Differential Equations (BSDEs) have been widely emp...

Rethinking ResNets: Improved Stacking Strategies With High Order Schemes

Various Deep Neural Network architectures are keeping massive vital reco...

Itô-Taylor Sampling Scheme for Denoising Diffusion Probabilistic Models using Ideal Derivatives

Denoising Diffusion Probabilistic Models (DDPMs) have been attracting at...