Strong Convergence of the Split-Step θ -Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes

Abstract

We develop a new split-step $\theta$ (SS$\theta$) method for stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the SS$\theta$ method for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory.