Numerical Solution of Multidimensional Exponential Levy Equation by Block Pulse Function

Subject Areas : Numerical Methods in Mathematical Finance

Minoo  Bakhshmohammadlou ¹ (Department of Mathematics, Iran University of Science and Technology, Tehran, Iran)
Rahman  Farnoosh ² (Department of Mathematics, Iran University of Science and Technology, Tehran, Iran)

Received: 2019-07-20 Accepted : 2020-01-28 Published : 2020-04-01

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

Abstract :

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 95% confidence interval by some numerical examples.‎

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