Optimal insurance in the presence of reinsurance

Sheng Chao Zhuang, Tim J. Boonen, Ken Seng Tan, Zuoquan Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


Published by Informa UK Limited, trading as Taylor & Francis Group. This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution.
Original languageEnglish
Pages (from-to)535-554
Number of pages20
JournalScandinavian Actuarial Journal
Issue number6
Publication statusPublished - 3 Jul 2017


  • competition constraint
  • Contract design
  • distortion risk measures
  • insurance
  • premium constraint
  • reinsurance

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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