Stepping Stone Symposium on Theoretical and Numerical Analysis of Partial Differential Equations with Specific Applications , 2017-08-29

Title : ( On accuracy and unconditional stability of an explicit Milstein finite difference scheme for a financial SPDE )

Authors: Mahdieh Arezoomandan , Ali Reza Soheili ,

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This article describes a new Milestein finite difference scheme based on alternating direction methods for a stochastic partial differential equation (SPDE) in portfolio credit modelling. The stochastic evolution equation describes a large particle system and the mathematical model was first motivated by [1]. The aim of this work is to present an efficient stochastic stable finite difference technique where the drift and double Ito integral are taken explicit. The stability and convergence analysis are based on Fourier analysis and it is shown that the proposed method is unconditional stable covering all arbitrary parameters of the SPDE model. The principal significance of the proposed method is that allows us to refine mesh size in computational domain and we do not require the solution of large systems of simultaneous equations at each time step. Numerical experiment is presented

Keywords

, stochastic partial differential equations, financial mathematics, finite difference, stability, convergence, Credit portfolio
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@inproceedings{paperid:1064141,
author = {Arezoomandan, Mahdieh and Soheili, Ali Reza},
title = {On accuracy and unconditional stability of an explicit Milstein finite difference scheme for a financial SPDE},
booktitle = {Stepping Stone Symposium on Theoretical and Numerical Analysis of Partial Differential Equations with Specific Applications},
year = {2017},
location = {ژنو},
keywords = {stochastic partial differential equations; financial mathematics; finite difference; stability; convergence; Credit portfolio models},
}

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%0 Conference Proceedings
%T On accuracy and unconditional stability of an explicit Milstein finite difference scheme for a financial SPDE
%A Arezoomandan, Mahdieh
%A Soheili, Ali Reza
%J Stepping Stone Symposium on Theoretical and Numerical Analysis of Partial Differential Equations with Specific Applications
%D 2017

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