The Poisson Log-Bilinear Lee-Carter Model

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractLife insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. As regards the latter, recent work has focused on modelling the trend in mortality as a stochastic process. A popular method for modelling death rates is the Lee-Carter model. This methodology has become widely used and there have been various extensions and modifications proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way, the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their Solvency Capital Requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company's financial position, expressing the degree to which the liabilities are covered by the assets.

Investigating Mortality Uncertainty Using the Block Bootstrap

“…Better bootstrap prediction intervals have been proposed see, e.g., 16 , but any improvement in accuracy will depend heavily on the validity of the Lee-Carter model assumption. See also D'Amato et al 17 for a stratified bootstrap sampling method which reduces simulation error.…”

Space, mortality, and economic growth

“…The process of aging of a population yields a change in the relative number of retirees compared to the number of active workers, which given political constraints of taxation, can create financial uncertainty for these institutions. That is why the ability to understand human survivorship is essential for actuarial, economic, and demographic practices, especially with regards to mortality modeling (Li & O'Hare, 2019; Renshaw & Haberman, 2003; Seklecka et al, 2017), annuity pricing (D'Amato et al, 2011; Pitacco, 2016), and social security affordability (Soneji & King, 2012).…”

Deepening Lee-Carter for longevity projections with uncertainty estimation

“…In particular, bootstrap procedures seem to represent the more tempting alternative since they do not require stringent sampling assumptions, allowing for accurate plug-in estimates (Efron and Tibshirani (1993)). In fact, such an approach have become a common practice to measure uncertainty in stochastic mortality models, as emerged in Brouhns et al (2005), Koissi et al (2006), Li et al (2009), D'Amato et al (2011), D'Amato et al (2012a) and D'Amato et al (2012b. However, to the best of our knowledge, machine and deep learning literature in mortality forecasting lack for studies about uncertainty estimation.…”