Numerical Solution of Multidimensional Exponential Levy Equation by Block Pulse Function

The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a ۹۵% confidence interval by some numerical examples.‎

Keywords:

Exponential Levy equation , Block Pulse Function , Operational matrix , Jump-diffusion market