Constrained Non-Concave Utility Maximization: An Application to Life Insurance Contracts with Guarantees

37 Pages Posted: 11 Aug 2017 Last revised: 6 May 2018

An Chen

University of Ulm

Peter Hieber

University of Ulm - Department of Mathematics and Economics

Thai Nguyen

University of Ulm - Institute of Insurance Science

Date Written: April 30, 2018

Abstract

We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insurance contracts. Deriving closed-form solutions, we observe that the fair pricing constraint will reduce the riskiness of the optimal strategies substantially. In an extensive numerical section, we analyze innovative retirement products that adapt the investment strategy of the premium pool according to the policyholder's preferences, modeled as constant relative risk aversion (CRRA). Such products are a response to the loss of attractiveness of traditional life insurance contracts with guarantees that are negatively affected by increasing solvency requirements for return guarantees and a general decrease in interest rate levels. Taking into account that retirement products are usually tax-privileged, we find that fairly priced guarantee contracts that follow this optimal investment strategy lead to a higher expected utility level than asset investments.

Keywords: optimal asset alllocation, insurance contract design, investment guarantee, utility maximization

JEL Classification: G11, G23

Suggested Citation

Chen, An and Hieber, Peter and Nguyen, Thai, Constrained Non-Concave Utility Maximization: An Application to Life Insurance Contracts with Guarantees (April 30, 2018). Available at SSRN: https://ssrn.com/abstract=3016267 or http://dx.doi.org/10.2139/ssrn.3016267

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

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

Peter Hieber (Contact Author)

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

Helmholzstrasse
Ulm, D-89081
Germany

Thai Nguyen

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

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