Modeling Joint Lives within Families

TL;DR

This paper investigates dependencies in life lengths within families using historical data, revealing significant correlations that impact actuarial calculations like annuities and insurance premiums.

Contribution

It introduces a novel analysis of parent-child and grandparent-grandchild life length dependencies using 19th century French family trees, extending beyond traditional joint life studies.

Findings

Positive association between parent and child life lengths.

Implications for life expectancy and annuity calculations.

Weaker but notable dependencies involving grandparents.

Abstract

Family history is usually seen as a significant factor insurance companies look at when applying for a life insurance policy. Where it is used, family history of cardiovascular diseases, death by cancer, or family history of high blood pressure and diabetes could result in higher premiums or no coverage at all. In this article, we use massive (historical) data to study dependencies between life length within families. If joint life contracts (between a husband and a wife) have been long studied in actuarial literature, little is known about child and parents dependencies. We illustrate those dependencies using 19th century family trees in France, and quantify implications in annuities computations. For parents and children, we observe a modest but significant positive association between life lengths. It yields different estimates for remaining life expectancy, present values of annuities, or whole life insurance guarantee, given information about the parents (such as the number of parents alive). A similar but weaker pattern is observed when using information on grandparents.