Investigating Mortality Uncertainty Using the Block Bootstrap

Abstract

This paper proposes a block bootstrap method for measuring mortality risk under the Lee-Carter model framework. In order to take account of all sources of risk the process risk, the parameter risk, and the model risk properly, a block bootstrap is needed to cope with the spatial dependence found in the residuals. As a result, the prediction intervals we obtain for life expectancy are more accurate than the ones obtained from other similar methods. 4Journal of Probability and Statistics Estimation of the ParametersInstead of using least-squares estimation via a singular value decomposition SVD to estimate a x , b x , and k t as in the original Lee and Carter paper, we adopt the methodology proposed by Brouhns et al. 12 . The main drawback of the SVD method is that the errors xt in 3.1 are assumed to be homoscedastic, which is not realistic. In order to circumvent the problems associated with the SVD method, Brouhns et al. 12 proposed the Poisson assumption to be applied to the death counts D xt . That is,

A General Procedure for Constructing Mortality Models

“…13 Nevertheless, for simplicity, 13 More recently, stratified (see D'Amato et al (2011)) and block-bootstrapping (see Liu and Braun (2010)) procedures have been used, as have those based on geo-statistical techniques which look at the correlation structure across residuals (see Debón et al (2008Debón et al ( , 2010). …”

Computational framework for longevity risk management

“…Ignoring dependency risk (D'Amato et al 2012) would lead to an inefficient risk management strategy for insurance companies. In particular, the presence of spatial dependence across age and time leads to a systematic over-estimation or under-estimation of uncertainty in the estimates, caused by whether negative or positive dependence dominates (Liu et al 2010). As is well-known in the demographic literature, the Lee Carter model has become the seminal statistical model for projections of mortality.…”

“…The increasing complexity of the real world imposes the necessity of modeling of dependent risks, so that, in the case of longevity data, the interactions between age and time cannot be neglected. Indeed, the presence of spatial dependence across age and time leads to systematic overestimation or under-estimation of uncertainty in the estimates, caused by whether negative or positive dependence dominates (Liu et al 2010). Thus, in order to produce accurate longevity projections, it is necessary to allow for the so-called dependency risk (D'Amato et al 2012).…”

“…In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the "lack of dependence" . By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence.…”

“…In the block bootstrap, however, instead of single observations, blocks of consecutive observations are drawn. This is done in order to capture the dependency structure of neighbouring observations (Liu and Braun 2010). In the literature, there is considerable evidence that the sieve bootstrap, initially proposed by Kreiss (1992) and Bulhmann (1997), usually outperforms the block bootstrap (Choi and Hall 2000).…”