TY - JOUR
ID - 671048
TI - Numerical Solution of Multidimensional Exponential Levy Equation by Block Pulse Function
JO - Advances in Mathematical Finance and Applications
JA - AMFA
LA - en
SN - 2538-5569
AU - Bakhshmohammadlou, Minoo
AU - Farnoosh, Rahman
AD - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 247
EP - 259
KW - Exponential Levy equation
KW - Block Pulse Function
KW - Operational matrix
KW - Jump-diffusion market
DO - 10.22034/amfa.2020.1873599.1260
N2 - 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.
UR - http://amfa.iau-arak.ac.ir/article_671048.html
L1 - http://amfa.iau-arak.ac.ir/article_671048_014eef581dc3c7325e5718a561ea632c.pdf
ER -