Discussion of Mortality Compression and Longevity Risk Discussed by Yijia Lin University of Nebraska - Lincoln Fifth International Longevity Risk and Capital Markets Solutions Conference September 26, 2009

Rectangularization vs. Steady Progress

Five Measures Mode age (M)  The age has the largest value of dx Probability of premature death  P(0≤X≤m), m=10, 20, 30, 40, 50 The smallest number of ages covers the probability of death (C α )  P(x≤X≤x+δ)= α Variance of age distribution for deaths (σ) The survival probability beyond a high age  P(X>M+k σ) where M is the mode age

Why measures computed with raw data is superior to those based on graduation methods? Graduation Methods Raw data Weighted least square to compute the variance of age distribution for death – Potential problem: the weight estimation for extreme values using only a few observations. High fluctuations for the probability of surviving beyond very high age – Mortality steady progress?

Questions to be addressed… How sensitive are the results based on raw data to the sample size? Are the results based on the raw data reliable?  “…we propose measurements to evaluation mortality compression based on the raw data, in order to reduce the influence of graduation. Still, the insufficient samples of the elderly cause fluctuations in the measurements…” Compare the graduation method and the proposed method for the same countries and prove the superiority of the proposed method Why should we concentrate on “the part with more confidence” (i.e. age up to M+2σ) when we deal with longevity risk?