| The solvency of a life insurance company is its capacity to fulfill its due responsibility according to the contracts at any time. The adequacy of solvency has strong relationships with more than a few important matters, ranging from the business qualification of an insurance company, whether it is able to satisfy its promise to the policyholders, to the healthy and sustainable development of the whole insurance industry. Solvency is of central importance to all parties involved, no matter the government regulator, the existing or prospective policyholders, or the insurance company itself. However, there are so many influential factors to consider that it is fairly complicated to evaluate the solvency directly, not to mention the poor feasibility due to high evaluation cost. As a result, what is evaluated in reality is the solvency margin, an integrated index of solvency.In this paper, we construct an optimal solvency margin model with respect to the traditional insurance business. The article gives a sufficient condition for the solvability of a related optimal problem, proves the existence and uniqueness of the solution of this optimal problem, and locates an approximate solution to it. Unlike most already existing studies, which are based on fixed interest rates, the optimal model proposed here is market-consistent so that its practicality is enhanced to some extent. At last this article holds a numerical analysis to three important life insurance businesses to reveal the drawback of coarse risk-classification existing in China’s prevailing computation method of solvency margin. In contrast with this drawback, our optimal solvency margin model is able to provide a much more reasonable, case-on-case solvency margin for insurance businesses containing various degrees of mortality fluctuation risks. Considering this, this paper has some reference value for both the government regulators and the insurance companies in China to optimize the related index of solvency margin. |
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