死亡率模型:長壽風險管理之應用

Mortality Models: An Application to Longevity Risk Management

林子綾(Tzu-Ling Lin)

指導教授 ： 曾郁仁

國立臺灣大學/管理學院/財務金融學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.00402

摘要

本論文包含兩篇重點在死亡率模型與長壽風險應用之文章。第一篇提出用相加結構改進Ballotta and Haberman (2006)的模型，因為我們認為B&H 的模型會有兩個值得質疑的特性。我們進一步做模型在養老險與年金商品為因應長壽風險而提撥額外準備金之應用，比較我們模型與B&H的模型下之結果。
在第二篇裡，我們在第一篇模型之period-cohort波動率加入年齡特性成為age-period-cohort波動率，然後用英國女性死亡率資料實證估計這兩種波動率。我們也用實證估計出的波動率計算第一篇定義的資本適足比率(CAR)。

關鍵字

隨機死亡率 ； 波動率 ； 長壽風險 ； 死亡率風險 ； 年金

並列摘要

The dissertation contains two essays to focus on a mortality model and make an application to the management of longevity risk. The first essay proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006) since there are two questionable features in the B&H model. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.
The second essay incorporates age-specific effects into period-cohort volatilities in the first essay and empirically estimates the volatilities by using UK female mortality data. We also calculate the empirical capital adequacy ratio (CAR) defined in the first essay by using the empirical estimated age-period-cohort volatilities.

並列關鍵字

stochastic mortality ； volatilities ； longevity risk ； mortality risk ； annuity

參考文獻

Part I References

Ballotta, L., and Haberman, S., 2006. The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case. Insurance: Mathematics and Economics 38, 195-214.

Biffis, E., 2005. Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics 37, 443-468.

Blake, D., and Burrows, W., 2001. Survivor bonds: helping to hedge mortality risk. Journal of Risk and Insurance 63, 339-348.

Blake, D., Cairns, A., Dowd, K., and MacMinn, R., 2006. Longevity bonds: financialengineering, valuation, and hedging. Journal of Risk and Insurance 73, 647-672.