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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Liu Xiangdong & Mi Zeyu & Chen Huida, 2020. "A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions," Journal of Systems Science and Information, De Gruyter, vol. 8(1), pages 17-32, February.
    • Handle: 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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    References listed on IDEAS

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