Calibrating Gompertz in Reverse

40 Pages Posted: 12 Nov 2019 Last revised: 14 Feb 2020

See all articles by Moshe A. Milevsky

Moshe A. Milevsky

York University - Schulich School of Business

Date Written: November 5, 2019


This paper develops a computational framework for inverting Gompertz-Makeham (GM) hazard rates, in a manner consistent with a compensation law of mortality for heterogenous populations, to define a Longevity-Risk-adjusted Global (LRaG) Age. To illustrate its salience and relative magnitude, the paper implements and calibrates this framework using rates from the Human Mortality Database (HMD). Among other things, this paper demonstrates that when properly benchmarked, the {\em longevity-risk-adjusted global age} of a 55-year-old Swedish male is 48, whereas a 55-year-old Russian male is closer in age to 67. The paper also discusses the connection between the LRaG age and the related concept of *biological* age. In a world of growing mortality heterogeneity, a new and distinct LRaG age could be used for pension and retirement policy. Perhaps a salient and transparent metric that adjusts chronological age for longevity risk might help capture the public's attention, educate them and induce them to take action to increase the odds of retirement success, by, for example, working longer and retiring later.

Keywords: Pensions, Insurance, Retirement, Longevity, Biological Age

JEL Classification: G22

Suggested Citation

Milevsky, Moshe Arye, Calibrating Gompertz in Reverse (November 5, 2019). Available at SSRN: or

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3

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