A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions

Liu Xiangdong (), Mi Zeyu () and Chen Huida ()
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Liu Xiangdong: Department of Statistics, Jinan University, Guangzhou, 510632, China
Mi Zeyu: Department of Statistics, Jinan University, Guangzhou, 510632, China
Chen Huida: Department of Statistics, Jinan University, Guangzhou, 510632, China

Journal of Systems Science and Information, 2020, vol. 8, issue 1, 17-32

Abstract: Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching (JD-SDS-MS). This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation. Our work dedicates to analytical properties of solutions to this model. First, we give some properties of the solution, including existence, uniqueness, non-negative and global nature. Next, boundedness of first moment of the solution to this model is considered. Third, properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain. Last, we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.

Keywords: stachastic differential system; Markovian switching; jump-diffusion; analytical properties; numerical solutions (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:8:y:2020:i:1:p:17-32:n:2

DOI: 10.21078/JSSI-2020-017-16

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