死亡率模型:長壽風險管理之應用

Abstract

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)。

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.