求解寿险负债估价问题的有限差分法研究

Study on a Finite Difference Approach to the Valuation of Insurance Liabilities

对传统的参加寿险保单的估价建立了模型.根据保险合约的结构,运用未定权益的定价理论进行合约定价分析.合约的最终给付主要取决于在合约有效期内,保险公司资产收益的历史状况.虽然这种路径相关性避免了近似定价公式的推导过程,但是通过减少维数,并利用有限差分法同样可以准确地进行合约估价.

A model for the valuation of traditional participating life insurance policies is set up. These claims are characterized by their explicit interest rate guarantees and the various embedded option elements. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation. The eventual benefits from the contracts considered crucially depend on the history of returns on the insurance company′s assets during the contract period. This path-dependence prohibits the derivation of close-form valuation formulas but it is demonstrated that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts.