Mortality in a heterogeneous population - Lee-Carter's methodology

TL;DR

This paper proposes a stochastic mortality model based on Lee-Carter methodology, replacing the Poisson assumption with a negative binomial distribution to better fit historical death data in heterogeneous populations.

Contribution

It introduces a modified Lee-Carter model with a negative binomial distribution for deaths, improving accuracy over traditional Poisson-based models in heterogeneous populations.

Findings

Model with negative binomial distribution fits historical data better.

Enhanced mortality modeling for heterogeneous populations.

Potential improvements in risk management for life insurance.

Abstract

The EU Solvency II directive recommends insurance companies to pay more attention to the risk management methods. The sense of risk management is the ability to quantify risk and apply methods that reduce uncertainty. In life insurance, the risk is a consequence of the random variable describing the life expectancy. The article will present a proposal for stochastic mortality modeling based on the Lee and Carter methodology. The maximum likelihood method is often used to estimate parameters in mortality models. This method assumes that the population is homogeneous and the number of deaths has the Poisson distribution. The aim of this article is to change assumptions about the distribution of the number of deaths. The results indicate that the model can get a better match to historical data, when the number of deaths has a negative binomial distribution.