Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps

摘要

The aim of this paper is to construct a numerical method to preserve positivity and mean-square dissipativity of stochastic age-dependent capital system with Poisson jumps. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the balanced implicit method(BIM) preserves positivity and converges with order 12 under given conditions. In addition, some sufficient conditions are obtained for ensuring the system and the balanced implicit method(BIM) are mean-square dissipative. Finally, a numerical example is simulated to illustrate the efficiency of theoretical results.