Multiple mortality modeling in Poisson Lee–Carter framework

Valeria D'Amato,Steven Haberman,Gabriella Piscopo,Maria Russolillo,Lorenzo Trapani

doi:10.1080/03610926.2014.960580

Abstract

ABSTRACTThe academic literature in longevity field has recently focused on models for detecting multiple population trends (D'Amato et al., 2012b; Njenga and Sherris, 2011; Russolillo et al., 2011, etc.). In particular, increasing interest has been shown about “related” population dynamics or “parent” populations characterized by similar socioeconomic conditions and eventually also by geographical proximity. These studies suggest dependence across multiple populations and common long-run relationships between countries (for instance, see Lazar et al., 2009). In order to investigate cross-country longevity common trends, we adopt a multiple population approach. The algorithm we propose retains the parametric structure of the Lee–Carter model, extending the basic framework to include some cross-dependence in the error term. As far as time dependence is concerned, we allow for all idiosyncratic components (both in the common stochastic trend and in the error term) to follow a linear process, thus considering a highly flexible specification for the serial dependence structure of our data. We also relax the assumption of normality, which is typical of early studies on mortality (Lee and Carter, 1992) and on factor models (see e.g., the textbook by Anderson, 1984). The empirical results show that the multiple Lee–Carter approach works well in the presence of dependence.

Highlights

The whole financial system is dramatically threatened by the systematic improvements in longevity phenomenon, especially regarding the welfare and public pensions
Securitization of longevity risk, i.e. the transfer of longevity risk in the capital markets, which typically occurs through the creation of derivatives or securities whose cash flows are linked to the survival of a reference population, a more effective risk management can be obtained throughout the study of the mortality correlations between populations
Standard Sieve bootstrap algorithm, since, when resampling the estimated common factors, a generated regressors problem arises. In this order of ideas, our paper is based on Trapani (2012), which develops the full blown theory to apply Sieve bootstrap to the context of non-stationary panel factor series, developing selection rules for the order of the VAR and showing the superior performance of Sieve bootstrap compared to first-order asymptotic

Summary

Introduction

The whole financial system is dramatically threatened by the systematic improvements in longevity phenomenon, especially regarding the welfare and public pensions. In the same context MacMinn et al 2013 are the first to apply the factor copula model to mortality fitting for multiple populations They focus on the residual risk (tail dependence) by setting out an efficient approach for high dimensional data. In a previous paper (D'Amato et al 2012b), we stated that in our context we cannot apply a standard Sieve bootstrap algorithm, since, when resampling the estimated common factors, a generated regressors problem arises. In this order of ideas, our paper is based on Trapani (2012), which develops the full blown theory to apply Sieve bootstrap to the context of non-stationary panel factor series, developing selection rules for the order of the VAR and showing the superior performance of Sieve bootstrap compared to first-order asymptotic.

Multiple Setting

The Poisson log-bilinear mortality model

Algorithm

Numerical Application

Concluding Remarks