The Lee-Carter mortality model provides the very first model for modeling the mortality rate with stochastic time and age mortality dynamics. The model is constructed modeling the mortality rate to incorporate both an age effect and a period effect. The Lee-Carter model provides the fundamental set up currently used in most modern mortality modeling. Various extensions of the Lee-Carter model include either adding an extra term for a cohort effect or imposing a stochastic process for mortality dynamics. Although both of these extensions can provide good estimation results for the mortality rate, applying them for the pricing of the mortality/ longevity linked derivatives is not easy. While the current stochastic mortality models are too complicated to be explained and to be implemented, transforming the cohort effect into a stochastic process for the pricing purpose is very difficult. Furthermore, the cohort effect itself sometimes may not be significant. We propose using a new modified Lee-Carter model with a Normal Inverse Gaussian (NIG) Lévy process along with the Esscher transform for the pricing of mortality/ longevity linked derivatives. The modified Lee-Carter model, which applies the Lee-Carter model on the growth rate of mortality rates rather than the level of mortality rates themselves, performs better than the current mortality rate models shown in Mitchell et al (2013). We show that the modified Lee-Carter model also retains a similar stochastic structure to the Lee-Carter model, so it is easy to demonstrate the implication of the model. We proposed the additional NIG Lévy process with Esscher transform assumption that can improve the fit and prediction results by adapting the mortality improvement rate. The resulting mortality rate matches the observed pattern that the mortality rate has been improving due to the advancing development of technology and improvements in the medical care system. The resulting mortality rate is also developed under a martingale measure so it is ready for the direct application of pricing the mortality/longevity linked derivatives, such as q-forward, longevity bond, and mortality catastrophe bond. We also apply our proposed model along with an information theoretic optimization method to construct the pricing procedures for a life settlement. While our proposed model can improve the mortality rate estimation, the application of information theory allows us to incorporate the private health information of a specific policy holder and hence customize the distribution of the death year distribution for the policy holder so as to price the life settlement. The resulting risk premium is close to the practical understanding in the life settlement market.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20504号 / 情博第632号 / 新制||情||110(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 鹿島 久嗣, 教授 山本 章博, 教授 阿久津 達也 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The objective of this thesis is to find patterns trends and assumptions for mortality vs. age prediction. Based on the analysis of trends in the already extinct cohorts, the most suitable models for estimating the future development of mortality among surviving cohorts are selected. This thesis compares real data extinct cohorts with balanced data Gompertz-Makehamovy function. The research and analysis is focused on the specifics of cohort mortality from the age of 90. The last part of this thesis illustrates comparison between real data of extinct cohorts with DeRaS model outputs. The selection of Kannisto and Thatcher as the optimal model is presented in the form of graphical outputs indicating the cohort life expectancy of men and women aged 90 years.