摘要
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.
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.
基金
Supported by the National Natural Science Foundation of China(71471075)
Fundamental Research Funds for the Central University(19JNLH09)
Humanities and Social Sciences Foundation of Ministry of Education,China(14YJAZH052).
