# Forecasting age distribution of death counts: An application to annuity pricing

## TL;DR

This paper introduces a compositional data analysis method for forecasting age-specific death counts, demonstrating superior accuracy over traditional models and aiding in annuity pricing and demographic estimations.

## Contribution

The paper presents a novel compositional data analysis approach that improves forecasting accuracy of age-specific death counts compared to existing methods.

## Key findings

- Outperforms Lee-Carter and Hyndman-Ullah methods in forecast accuracy
- Provides more reliable estimates for survival probabilities and life expectancy
- Enhances annuity pricing accuracy for various ages and maturities

## Abstract

We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data analysis approach produces more accurate one- to 20-step-ahead point and interval forecasts than Lee-Carter method, Hyndman-Ullah method, and two na\"{i}ve random walk methods. The improved forecast accuracy of period life-table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities. Although we focus on temporary annuity prices, we consider long-term contracts which make the annuity almost lifetime, in particular when the age at entry is sufficiently high.