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Tonuity: A Novel Individual-Oriented Retirement Plan

30 Pages Posted: 28 Sep 2017  

An Chen

University of Ulm

Peter Hieber

University of Ulm - Department of Mathematics and Economics

Jakob Klein

University of Ulm - Department of Mathematics and Economics

Date Written: September 26, 2017

Abstract

For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (for example conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company's role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder's viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity's payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder's lifetime utility.

Keywords: longevity risk, tontines, pooled annuities, capital requirements, lifetime utility

Suggested Citation

Chen, An and Hieber, Peter and Klein, Jakob, Tonuity: A Novel Individual-Oriented Retirement Plan (September 26, 2017). Available at SSRN: https://ssrn.com/abstract=3043013

An Chen

University of Ulm ( email )

Helmholzstrasse
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Peter Hieber

University of Ulm - Department of Mathematics and Economics ( email )

Helmholzstrasse
Ulm, D-89081
Germany

Jakob Klein (Contact Author)

University of Ulm - Department of Mathematics and Economics ( email )

Helmholzstrasse
Ulm, D-89081
Germany

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