Tontines with Mixed Cohorts

34 Pages Posted: 18 Mar 2020 Last revised: 14 Nov 2020

See all articles by An Chen

An Chen

University of Ulm

Linyi Qian

affiliation not provided to SSRN

Zhixin Yang

Ball State University

Date Written: February 22, 2020


With the advancements of medical technology and the improvements in quality of life, the demand for innovative retirement products designed to address increasing longevity risks has been growing in recent decades. Tontines and tontine like products, where the insurers and policyholders share longevity risks, are being explored as an alternative to annuities. As of now, homogeneous policyholders are often assumed in the design process of this mortality-pooling product type. Inspired by the work of Milevsky and Salisbury [2016] in which heterogeneous cohorts are considered, we also extend the tontine products to heterogeneous policyholders. Different from the method employed in Milevsky and Salisbury [2016], we establish the explicit expression of optimal withdrawal rates under the actuarial fairness budget constraint held for one single cohort. In addition, we propose a numerical procedure to achieve approximate fairness among the cohorts by choosing participation rates (or the share prices) properly.

Keywords: longevity risk, tontines, mixed cohort, certainty equivalent payment, lifetime utility.

JEL Classification: C

Suggested Citation

Chen, An and Qian, Linyi and Yang, Zhixin, Tontines with Mixed Cohorts (February 22, 2020). Available at SSRN: or

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081


Linyi Qian (Contact Author)

affiliation not provided to SSRN

Zhixin Yang

Ball State University ( email )

Muncie, IN 47306-0340
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics