Demographic Issues in Longevity Risk Analysis

ABSTRACT Fundamental to the modeling of longevity risk is the specification of the assumptions used in demographic forecasting models that are designed to project past experience into future years, with or without modifications based on expert opinion about influential factors not represented in the historical data. Stochastic forecasts are required to explicitly quantify the uncertainty of forecasted cohort survival functions, including uncertainty due to process variance, parameter errors, and model misspecification errors. Current applications typically ignore the latter two sources although the potential impact of model misspecification errors is substantial. Such errors arise from a lack of understanding of the nature and causes of historical changes in longevity and the implications of these factors for the future. This article reviews the literature on the nature and causes of historical changes in longevity and recent efforts at deterministic and stochastic forecasting based on these data. The review reveals that plausible alternative sets of forecasting assumptions have been derived from the same sets of historical data, implying that further methodological development will be needed to integrate the various assumptions into a single coherent forecasting model. Illustrative calculations based on existing forecasts indicate that the ranges of uncertainty for older cohorts' survival functions will be at a manageable level. Uncertainty ranges for younger cohorts will be larger and the need for greater precision will likely motivate further model development. INTRODUCTION Longevity risk can be defined at individual and aggregate levels. At the individual level, longevity risk refers to the possibility of living longer than assumed in financial planning for the retirement of a single individual. At the aggregate level, longevity risk refers to the possibility of a higher average number of years of survival than assumed in designing a retirement security system for the aggregate. If the aggregate is a cohort of individuals who share a common year of birth, then, in theory, the longevity risk can be hedged with longevity bonds having coupons proportional to the number of cohort survivors at each anniversary after the issue date. Longevity bonds represent a potentially important new approach to the management of aggregate longevity risks. However, before such bonds or other similar instruments become practically feasible, a number of issues must be resolved. This article focuses on demographic issues in longevity risk analysis relating to the measurement and modeling of survival and mortality. Actuarial (Cox, Lin, and Wang, 2006; Cairns, Blake, and Dowd, 2006), economic (Turner, 2006; Brown and Orszag, 2006), and financial issues (Blake et al., 2006; Milevsky, Promislow, and Young, 2006) are addressed elsewhere in this issue of the Journal of Risk and Insurance. Among the demographic issues to be considered are the following: 1. Accurate measurements of the initial size and defining characteristics of each cohort, of decrements due to death, emigration, or other censoring events, and of increments due to immigration or other forms of cohort recruitment, are necessary to ensure that the longevity bond coupons accurately reflect the requirement that they be proportional to the number of survivors at each future date. 2. Accurate measurements of the inputs to the various models used for forecasting future survival and mortality are necessary for ensuring the validity of the outputs of those models. 3. New demographic models based on generalizations of the basic life table are needed for use in forecasting future survival and mortality. Factors to be considered in formulating such models include the following: * The impact of limits on the rate of increase in life expectancy and on the maximum value of life expectancy; * The changing nature of the mortality process; * The impact of individual-level risk covariates and their change over age, calendar time, and cohort; * The impact of technological innovation; * The stochasticity of life table parameters and its representation in forecasts. …