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

European Journal of Operational Research, Vol. 273, No. 3, pp. 1119-1135, 2019

40 Pages Posted: 11 Aug 2017 Last revised: 6 Dec 2018

See all articles by An Chen

An Chen

Ulm University - Institute of Insurance Science

Peter Hieber

Université de Lausanne

Thai Nguyen

Ulm University - 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). European Journal of Operational Research, Vol. 273, No. 3, pp. 1119-1135, 2019, Available at SSRN: https://ssrn.com/abstract=3016267 or http://dx.doi.org/10.2139/ssrn.3016267

An Chen

Ulm University - Institute of Insurance Science ( email )

Ulm, 89081
Germany

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

Peter Hieber (Contact Author)

Université de Lausanne ( email )

Lausanne
Switzerland

Thai Nguyen

Ulm University - Institute of Insurance Science ( email )

Ulm, 89081
Germany

Do you want regular updates from SSRN on Twitter?

Paper statistics

Downloads
189
Abstract Views
1,192
rank
217,853
PlumX Metrics