TY - JOUR

T1 - Mortality modeling and regression with matrix distributions

AU - Albrecher, Hansjörg

AU - Bladt, Martin

AU - Bladt, Mogens

AU - Yslas, Jorge

N1 - Publisher Copyright: © 2022 The Author(s)

PY - 2022

Y1 - 2022

N2 - In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can lead to reasonably accurate and relatively parsimonious models for mortality curves across the entire lifespan. A particular feature of the proposed model framework is that it allows for a more direct interpretation of the implied underlying aging process than some previous approaches. Subsequently, towards applications of the approach for multi-population mortality modeling, we introduce regression via the concept of proportional intensities, which are more flexible than proportional hazard models, and we show that the two classes are asymptotically equivalent. We illustrate how the model parameters can be estimated from data by providing an adapted EM algorithm for which the likelihood increases at each iteration. The practical feasibility and competitiveness of the proposed approach, including the right-censored case, are illustrated by several sets of mortality and survival data.

AB - In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can lead to reasonably accurate and relatively parsimonious models for mortality curves across the entire lifespan. A particular feature of the proposed model framework is that it allows for a more direct interpretation of the implied underlying aging process than some previous approaches. Subsequently, towards applications of the approach for multi-population mortality modeling, we introduce regression via the concept of proportional intensities, which are more flexible than proportional hazard models, and we show that the two classes are asymptotically equivalent. We illustrate how the model parameters can be estimated from data by providing an adapted EM algorithm for which the likelihood increases at each iteration. The practical feasibility and competitiveness of the proposed approach, including the right-censored case, are illustrated by several sets of mortality and survival data.

KW - Inhomogeneous Markov processes

KW - Inhomogeneous phase-type distributions

KW - Phase-type distributions

KW - Regression models

KW - Survival analysis

UR - http://www.scopus.com/inward/record.url?scp=85136478979&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2022.08.001

DO - 10.1016/j.insmatheco.2022.08.001

M3 - Journal article

AN - SCOPUS:85136478979

VL - 107

SP - 68

EP - 87

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -