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Socio-economic differentiation in experienced mortality modelling and its pricing implications
European Actuarial Journal ( IF 0.8 ) Pub Date : 2021-05-25 , DOI: 10.1007/s13385-021-00282-1
Ahmad Salahnejhad Ghalehjooghi , Pintao Lyu

In recent years, increasing availability and quality of the portfolio data enables the life insurers to render fair and flexible pricing based on individual-level socio-economic attributes. Yet, many insurers price based on the “experience factor”; portfolio-specific mortality divided by population mortality. We incorporate the logistic regression in the experience mortality model by Plat (Insurance 45:123–132, 2009) and examine the effect of the differentiating factor(s) on the level and trend of mortality. The regression model accounts for socio-economic factors, such as salary, in the portfolio and constructs the corresponding differentiated experience factors. To address the varying uncertainty in each class of the differentiated experienced mortality, we provide the price of a simple survival benefit for a cohort with and without differentiation. We employ the EIOPA risk-margin price to examine how the differentiated mortality can be reflected in the required risk-loading, using the salary as an example differentiator. Further, we extend the risk margin price to a “time-consistent” price to address the considerable likelihood of the middle-time dynamics of the experience mortality in long-dated contracts. The Least Square Monte Carlo (LSMC) method serves as the numerical method to calculate the conditional operators in the time-consistent price. We find that differentiation is significant for different salary classes. For example, for the 40 years old male cohort, salary differentiation can result in around 7% discount for the low salary class and 7.9% surcharge for the high salary class.



中文翻译:

有经验的死亡率模型中的社会经济差异及其对价格的影响

近年来,投资组合数据的可用性和质量不断提高,使人寿保险公司能够根据个人级别的社会经济属性进行公平,灵活的定价。然而,许多保险公司是根据“经验因素”来定价的。投资组合特定死亡率除以人口死亡率。我们将逻辑回归纳入Plat的经验死亡率模型中(保险45:123–132,2009),并研究了差异化因素对死亡率水平和趋势的影响。回归模型考虑了投资组合中的社会经济因素,例如工资,并构造了相应的差异化体验因素。为了解决不同类别的经历过的死亡率各不相同的不确定性,我们为有或没有分化的人群提供简单的生存利益的价格。我们使用EIOPA风险边际价格,以薪金为例,研究如何在所需的风险负担中反映差异化的死亡率。此外,我们将风险保证金价格扩展为“时间一致”价格,以解决长期合同中经验死亡率的中间时间动态变化的可能性。最小二乘蒙特卡洛(LSMC)方法是用于计算时间一致价格中条件算子的数值方法。我们发现,差异对于不同的薪资类别而言意义重大。例如,对于40岁的男性队列,低薪阶层的薪资差异可能会导致7%的折扣,高薪阶层的薪金差异会导致7.9%的附加费。我们使用EIOPA风险边际价格,以薪金为例,来研究差异化死亡率如何反映在所需的风险负担中。此外,我们将风险保证金价格扩展为“时间一致”价格,以解决长期合同中经验死亡率的中间时间动态变化的可能性。最小二乘蒙特卡洛(LSMC)方法是用于计算时间一致价格中条件算子的数值方法。我们发现,差异对于不同的薪资类别而言意义重大。例如,对于40岁的男性队列,低薪阶层的薪资差异可能会导致7%的折扣,高薪阶层的薪金差异会导致7.9%的附加费。我们使用EIOPA风险边际价格,以薪金为例,来研究差异化死亡率如何反映在所需的风险负担中。此外,我们将风险保证金价格扩展为“时间一致”价格,以解决长期合同中经验死亡率的中间时间动态变化的可能性。最小二乘蒙特卡洛(LSMC)方法是用于计算时间一致价格中条件算子的数值方法。我们发现,差异对于不同的薪资类别而言意义重大。例如,对于40岁的男性队列,低薪阶层的薪资差异可能会导致7%的折扣,高薪阶层的薪金差异会导致7.9%的附加费。

更新日期:2021-05-25
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