The positive numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm

Abstract We know that the exact solutions for most of stochastic age-structured capital systems are difficult to find. The numerical approximation method becomes an important tool to study properties for stochastic age-structured capital models. In the paper, we study the numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm and discuss the convergence of numerical solution. For the practical significance of capital, we need to consider the positivity of the numerical solution. Therefore, we introduce a penalty factor in the stochastic age-dependent capital system to maintain the positivity, and analyze the convergence of the positive numerical solution. Finally, an example is given to verify our theoretical results.

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