A wavelet method for stochastic Volterra integral equations and its application to general stock model

Document Type : Research Paper


Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran


In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation which can be solved by some numerical methods like Newton's or Broyden's methods. The capability of the simulation of Brownian motion with Schauder functions which are the integration of Haar functions enables us to find some reasonable approximate solutions. Two test examples and the application of the presented method for the general stock model are considered to demonstrate the efficiency, high accuracy and the simplicity of the presented method.


Volume 5, Issue 2 - Serial Number 2
April 2017
Pages 170-188
  • Receive Date: 11 August 2016
  • Revise Date: 18 November 2016
  • Accept Date: 14 December 2016
  • First Publish Date: 01 April 2017