A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

Abstract

In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.

Keywords

• weak order 2.0 scheme
• markovian switching
• malliavin calculus