Strong convergence of the split-step θ-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

• Main Authors: Ting Kang, Qimin Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2018-10-01
• Series: Advances in Difference Equations
• Subjects: Stochastic age-dependent capital system; Poisson jumps; Fractional Brownian motion; Split-step θ-method; Strong convergence
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1828-z

Abstract Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of stochastic age-dependent capital systems with Poisson jumps and fractional Brownian motion (fBm) and investigate the convergence of the split-step θ-method (SSθ) for this system. It is proved that the numerical approximation solutions converge to the analytic solutions for the equations, and the order of approximation is also provided. Finally, a numerical experiment is simulated to illustrate that the SSθ method has better accuracy than the Euler method.