A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps

Yang Li, Yaolei Wang, Taitao Feng and Yifei Xin
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Yang Li: 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
Taitao Feng: 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 3, 1-14

Abstract: In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we theoretically prove that the numerical scheme has second-order convergence rate. To demonstrate the effectiveness and the second-order convergence rate, three numerical experiments are given.

Keywords: weak second-order scheme; poisson process; Malliavin calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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