Modelling Italian mortality rates with a geometric-type fractional Ornstein-Uhlenbeck process

TL;DR

This paper introduces a novel stochastic model using fractional Ornstein-Uhlenbeck processes to capture long-term memory in Italian mortality rates, extending previous models driven by standard Brownian motion.

Contribution

It generalizes existing mortality models by incorporating fractional Brownian motion, revealing long-term memory effects in mortality hazard rates.

Findings

Mortality rates exhibit long-term memory effects.

The fractional model fits Italian mortality data from 1950 to 2004.

The model extends previous Brownian-motion-based approaches.

Abstract

We propose to model mortality hazard rates for human population using the exponential of the solution of a stochastic differential equation (SDE). The noise in the SDE is a fractional Brownian motion. We will use the well-known fractional Ornstein-Uhlenbeck process. Using the Hurst parameter we showed that mortality rates exhibit long-term memory. The proposed model is a generalization of the model introduced by [6], where they used an SDE driven with a Brownian motion. We tested our model with the Italian population between the years 1950 to 2004.