Numerical Solutions of Jump Diffusions with Markovian Switching

Details Numerical Solutions of Jump Diffusions with Markovian Switching Numerical Solutions of Jump Diffusions with Markovian Switching

2011-03-10

arxiv.org/abs/1103.2049v1

Mathematics

Numerical Analysis

21 pages, 1 figure

Scientific paper

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.

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