Convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes

摘要

In stochastic differential equations (SDEs), there is a class of stochastic functional differential equations with random jump magnitudes, which aries in many financial models. In general most equations of stochastic age-dependent capital system do not have explicit solutions. Thus numerical approximation schemes are invaluable tools for exploring their properties. In this paper, the numerical approximation is established for a class of stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the numerical approximation for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the numerical approximate solutions converge to the analytical solutions of the equations under given conditions. The numerical approximate results in Zhang et al. (2011) [2] are improved. An example is given for illustration.