A Comparative Analysis of Minimum Initial Capital Requirements in Discrete-Time Insurance Surplus Models

This study determines the requisite minimum initial capital for an insurance company to prevent bankruptcy, ensuring that the ruin probability does not exceed 0.01. We analyze discrete-time insurance surplus models across three categories: non-investment, bond investment, and stock investment. We examine the minimum initial capital necessary for non-investment, bond investment, and stock investment across various safety loadings. The ruin probabilities of three models are obtained through simulation, whereas the minimum initial capital is calculated using the linear least squares method. The results demonstrate that for safety loading levels ranging from 0.1 to 0.4, increasing by 0.1, the model's stock investment necessitates a reduced minimum initial capital in comparison to both non-investment and bond investment. For safety loading values ranging from 0.5 to 1.0, with increments of 0.1, the minimum initial capital for the three types is nearly identical.