在长寿风险对冲框架下,通过引入外生的产品价格,构建了基于价格调整的自然对冲模型。首先运用最优化理论得到了模型最优产品配比的解析式,然后在实际的销售配比与模型的最优配比相等的约束下,推导出了寿险产品和年金产品的最优定价。该定价能够使得模型的最优配比真正被实现,即销售的配比刚好是使产品组合长寿风险最小化的最优配比。最后通过数值算例,阐述了基于价格调整的自然对冲策略的效果,并进一步分析了利率、承保年龄、性别等因素对自然对冲策略的影响。
In the framework of longevity risk hedging, a price-adjusted longevity risk natural hedging model is established by introducing the exogenous product prices. Firstly, the analytical solution of the optimal product mix of the model is derived by adopting the optimization theory. Then, optimal prices for life insurance products and annuities are obtained under the constraint that the actual product mix equals to the optimal product mix of the model. Under the optimal prices, the optimal product mix of the model is truly realized, that is, the actual product mix is exactly the optimal product mix which minimizes the longevity risk. Finally, the effectiveness of the natural hedging strategy based on the effect of price adjustment is illustrated by using numerical examples. Furthermore, the impact of the interest rates, age and gender on the natural hedging strategy is also examined.
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