基于仿射模型的我国商业养老年金风险测度分析
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摘要
本文针对年金管理,综合考虑死亡率随年龄和时间的变动规律,构建基于我国历史数据的Gaussian-Gompertz随机死亡率模型,采用Vasicek模型刻画短期利率风险,采用几何布朗运动随机模型刻画权益风险,采用资产负债比率变异系数、破产概率和偿付能力风险资本系数等指标度量风险。研究发现:个体波动性长寿风险通过扩大投保规模将得到有效分散;集体趋势性长寿风险随时间的延续不断积聚;长寿风险、利率风险与投资风险的综合影响会显著增加保险公司的风险水平,危及公司的偿付能力;相比长寿风险,利率风险和投资风险对偿付能力风险的影响更大。
This paper combines the evolutions of mortality with age and time for annuity management and establishes a Gaussian-Gompertz stochastic mortality model based on the historical data of mortalities in China. Moreover, the interest rate follows the Vasicek model and the equity risk is modeled by a geometric Brownian motion. Meanwhile, this paper assesses the risks by the coefficient of variance of funding ratio, probability of ruin and solvency capital requirement. The analysis show that:the individual volatility longevity risk can be efficiently eliminated by increasing the size of the annuity; the group tendency longevity risk accumulates with time continuously; the combination of longevity risk, interest risk and investment risk increases risks of the insurance company significantly and imperils the solvency of the company; compared to longevity risk, the effects of interest risk and investment risk on the risk level are larger.
This paper combines the evolutions of mortality with age and time for annuity management and establishes a Gaussian-Gompertz stochastic mortality model based on the historical data of mortalities in China. Moreover, the interest rate follows the Vasicek model and the equity risk is modeled by a geometric Brownian motion. Meanwhile, this paper assesses the risks by the coefficient of variance of funding ratio, probability of ruin and solvency capital requirement. The analysis show that:the individual volatility longevity risk can be efficiently eliminated by increasing the size of the annuity; the group tendency longevity risk accumulates with time continuously; the combination of longevity risk, interest risk and investment risk increases risks of the insurance company significantly and imperils the solvency of the company; compared to longevity risk, the effects of interest risk and investment risk on the risk level are larger.
引文
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[12] Lee R D,Carter L R.Modeling and forecasting US mortality[J].Journal of the American Statistical Association,1992,87(419):659～671.
[13] Vasicek O.An equilibrium characterization of the term structure[J].Journal of Financial Economics,1977,5(2):177～188.
[2] 韩猛,王晓军.个人年金产品中蕴含的长寿风险研究[J].保险研究,2013,(6):52～58.
[3] 尚勤,秦学志.随机死亡率和利率下退休年金的长寿风险分析[J].系统工程,2009,27(11):56～61.
[4] 王晓军,赵明.中国高龄人口死亡率随机波动趋势分析[J].统计研究,2014,3(9).
[5] 徐英.论保险公司长寿风险管理的困境与对策[J].生产力研究,2012,(9):75～77.
[6] 张连增,段白鸽.CIR利率模型下永久年金现值变量的分布模拟[J].系统工程学报,2014,29(1):56～65.
[7] 张颖,黄顺林.基于随机死亡率与利率模型下的生存年金组合风险分析[J].系统工程,2010,28(9):15～19.
[8] Biffis E.Affine processes for dynamic mortality and actuarial valuations[J].Insurance:Mathematics and Economics,2005,37(3):443～468.
[9] Duan J C,Simonato J G.Estimating and testing exponential-affine term structure models by Kalman filter[J].Review of Quantitative Finance and Accounting,1999,13(2):111～135.
[10] Hari N,et al.Longevity risk in portfolios of pension annuities[J].Insurance:Mathematics and Economics,2008,42(2):505～519.
[11] Jevtic P,Regis L.Assessing the solvency of insurance portfolios via a continuous-time cohort model[J].Insurance:Mathematics and Economics,2015,61:36～47.
[12] Lee R D,Carter L R.Modeling and forecasting US mortality[J].Journal of the American Statistical Association,1992,87(419):659～671.
[13] Vasicek O.An equilibrium characterization of the term structure[J].Journal of Financial Economics,1977,5(2):177～188.