Exponential stability of numerical solutions for a class of stochastic age-dependent capital system with Poisson jumps

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring its properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Poisson jumps, and investigate the convergence of numerical approximation. It is proved that the the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. A numerical example is provided to illustrate the theoretical results.