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

Yang Li, Taitao Feng, Yaolei Wang and Yifei Xin
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Yang Li: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Taitao Feng: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Yaolei Wang: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Yifei Xin: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Mathematics, 2021, vol. 9, issue 6, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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