Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching

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 Markovian switching, and investigate the convergence of numerical approximation. It is proved that 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.

Research Highlights► We give a class of stochastic age-dependent capital system with Markovian switching. ► We investigate the convergence of numerical approximation. ► Convergence theorems for the approximation of the solution by Euler scheme are proved. ► This article provides the effective method for calculating the capital.