Optimal capital allocation for individual risk model using a Mean-Variance Principle

Abstract

<p style='text-indent:20px;'>In this article, we study the problem of optimal capital allocation for the individual risk model using the Mean-Variance principle with quadratic loss function when a total amount of initial capital is granted for allocation. The determination of the optimal capital allocation strategy proceeds in two phases. First, explicit formulas for the optimal allocations are presented based on the assumption that the claim occurrence indicators are independent of the claim severities when the allocated total capital is fixed. Second, an approximating algorithm is proposed to find out the optimal value of capital used for allocation through minimizing the mean-variance loss function. As a result, the exact allocation policy can be provided by following the first phase again. Numerical examples and applications are provided to illustrate the main results and some discussions on the effect of neglecting the dependence between the claim occurrence indicators and claim severities on the optimal allocations are also given to shed light on future research.</p>