Applying spectral biclustering to mortality data

Gabriella Piscopo,Marina Resta

doi:10.3390/risks5020024

Abstract

We apply spectral biclustering to mortality datasets in order to capture three relevant aspects: the period, the age and the cohort effects, as their knowledge is a key factor in understanding actuarial liabilities of private life insurance companies, pension funds as well as national pension systems. While standard techniques generally fail to capture the cohort effect, on the contrary, biclustering methods seem particularly suitable for this aim. We run an exploratory analysis on the mortality data of Italy, with ages representing genes, and years as conditions: by comparison between conventional hierarchical clustering and spectral biclustering, we observe that the latter offers more meaningful results.

Highlights

During the last decade, the analysis of mortality datasets has been deepened by actuaries and statisticians
We considered the death rates of the whole Italian population; the data were downloaded from the Human Mortality Database 1 (HMD)
This approach can be motivated by the attention devoted to mortality investigations: the accurate modeling and projection of mortality rates and life expectancy, are of growing interest to researchers because of their impact on actuarial liabilities of private life insurance companies, pension funds and national pension systems; in this respect, it makes sense to monitor the extent to which the longevity improvements is meaningful

Summary

Introduction

The analysis of mortality datasets has been deepened by actuaries and statisticians. The growing attention devoted to mortality investigation is due to the financial impact on actuarial liabilities of private life insurance companies, pension funds and national pension systems: as a matter of fact, monthly pension payments are generally based on remaining life expectancy at retirement; the accurate modeling and projection of mortality rates and life expectancy are of growing interest to researchers. In this respect, it makes sense to monitor how much longevity improvements are sizeable: it has been noted that, in the past century survival, probabilities have increased for each age group, even though with some undeniable differences. The fit to historical data is made through the Singular Value Decomposition (SVD) [2] of M, and the time-varying parameter is modeled and forecasted as an ARIMA process using standard Box-Jenkins methodology

Results

Discussion

Conclusion