Numerical Solutions of Jump Diffusions with Markovian Switching

TL;DR

This paper develops a new Euler-based numerical algorithm for jump diffusions with Markovian switching, proving its convergence and error order, supported by numerical experiments demonstrating efficiency.

Contribution

Introduces a jump-adapted Euler scheme for jump diffusions with Markovian switching, establishing convergence and error bounds.

Findings

The numerical scheme converges to the exact solution.

Error order of the scheme is derived.

Numerical experiments confirm computational efficiency.

Abstract

In this paper we consider the numerical solutions for a class of jump diffusions with Markovian switching. After briefly reviewing necessary notions, a new jump-adapted efficient algorithm based on the Euler scheme is constructed for approximating the exact solution. Under some general conditions, it is proved that the numerical solution through such scheme converge to the exact solution. Moreover, the order of the error between the numerical solution and the exact solution is also derived. Numerical experiments are carried out to show the computational efficiency of the approximation.