Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes

Mathematical and Computational Applications

Iyigunler, Ismail¹ 

关键词: Stochastic differential equations;    Levy processes;    Stochastic integrating factors;    Linearization;   

DOI  :  10.3390/mca17010068

学科分类：计算数学

来源: mdpi

【 摘 要 】

We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.

【 授权许可】

CC BY