带有破产时刻的新款变额年金定价研究  

Pricing a New Guaranteed Benefit in Variable Annuities with Bankruptcy Moment

作　　者：王苏鑫 张樱露 宫晶 Wang Suxin;Zhang Yinglu;Gong Jing(College of Science,Civil Aviation University of China,Tianjin 300300,China;School of Mathematics and Statistics,Nanjing University of Science&.Technology,Nanjing 210094,China)

机构地区：[1]中国民航大学理学院,天津300300 [2]南京理工大学数学与统计学院,江苏南京210094

出　　处：《南开大学学报（自然科学版）》2022年第6期36-47,57,共13页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the Scientific Research Project of Tianjin Educational Committee(2019KJ131)。

摘　　要：开发了一款新的附加在可变年金(VA)上的最小权益保证条款,可以被视为由最低到期权益保证、最低身故权益保证和最低提款权益保证的组合条款,记为最低死亡和到期提取权益保证.通过研究保险公司的可能损失,在无套利假设和随机死亡率、利率的前提下给出了用两种不同估值方法得到的公平保费的解析表达式.通过详细考虑投保人投资账户的破产时刻给出了公平保费的估值,并与传统经典估值方法进行了比较.使用蒙特卡罗方法模拟并比较了两种方法下的保险公司损失和公平保费.结论是,传统定价方法夸大了投保人投资账户提前破产的可能性,从而增加了保险公司极端预期损失的可能.A new portfolio guaranteed minimum benefit option is developed that can be seen as consisting of a guaranteed minimum maturity benefit, a guaranteed minimum death benefit and a guaranteed minimum withdrawal benefit, recorded as guaranteed minimum death and withdrawal benefit. By studying the possible losses of insurance company, the closed form of the fair fee are given by two different valuing methods under the premise of no arbitrage assumption, random mortality rate and interest rate. The fair premium valuing method by considering the bankruptcy moment of policyholder’s investment account is compared with the traditional classic valuing method. Monte Carlo method is used to simulate and compare the insurer’s loss and fair cost obtained by the two different methods. The traditional pricing method overstates the likelihood that the investment account will go bankrupt at an early time, thereby increasing the possibility of extreme expected losses of insurance company.

关 键 词：组合期益 最低到期权益保证 最低提款权益保证 随机死亡率 随机利率 

分 类 号：O211.63[理学—概率论与数理统计] F840[理学—数学]