Article2019

An Arbitrary High Order Weak Approximation of SDE and Malliavin Monte Carlo: Analysis of Probability Distribution Functions

32 citations0/0 files storedSIAM Journal on Numerical Analysis

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Stochastic processes and financial applications Numerical methods for differential equations Mathematical Approximation and Integration

Abstract

This paper provides an arbitrary high order weak approximation scheme for multidimensional Stratonovich stochastic differential equations using Malliavin calculus. The scheme efficiently works whether the test function is smooth or not. The Malliavin Monte Carlo method, a simple numerical algorithm, is introduced to implement the scheme. Numerical examples illustrate the validity of the method.

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2008Multilevel Monte Carlo Path Simulation 1996The law of the Euler scheme for stochastic differential equations 1987Analysis of Wiener Functionals (Malliavin Calculus) and its Applications to Heat Kernels 2004Cubature on Wiener space 2008Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing 2018Approximation of Expectation of Diffusion Process and Mathematical Finance 2009On irregular functionals of SDEs and the Euler scheme 2012An Asymptotic Expansion with Push-Down of Malliavin Weights

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