Investigating Mortality Uncertainty Using the Block Bootstrap.pdf

Hindawi Publishing Corporation Journal of Probability and Statistics Volume 2010, Article ID 813583, 15 pages doi: Research Article Investigating Mortality Uncertainty Using the Block Bootstrap Xiaoming Liu and W. John Braun Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada N6A 5B7 Correspondence should be addressed to Xiaoming Liu, ******@ Received 14 August 2010; Accepted 10 December 2010 Academic Editor: Rongling Wu Copyright q2010 X. Liu and W. J. Braun. This is an open access article distributed under the mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction For actuarial pricing and reserving purposes, the mortality table needs to be projected to allow for improvement in mortality to be taken into account. It is now a well-accepted fact that mortality development is di ?cult to predict; therefore, a stochastic mortality modelling approach has been advocated ? 1 , 2 ?. For a review of recent developments in stochastic mortality modelling, interested readers are referred to o ? 3 ?and Cairns et al. ? 4 ?. Under the framework of a stochastic mortality model, future mortality rates are random as are the other quantities derived from the mortality table. In order to manage the mortality risk properly, we need to assess the ing from the mortality dynamics carefully. There are three types of risk embedded in adopting a stochastic mor