Constrained non-concave utility maximization: An application to life insurance contracts with guarantees

An Chen, Peter Hieber, Thai Nguyen

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish
Pages (from-to)1119-1135
Number of pages17
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 16 Mar 2019
Externally publishedYes


  • Insurance contract design
  • Logarithmic utility
  • Managerial compensation
  • Optimal asset allocation
  • Power utility


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