Budget-constrained optimal reinsurance design under coherent risk measures

Ka Chun Cheung, Wing Fung Chong, Ambrose Lo

Research output: Contribution to journalArticlepeer-review


Reinsurance is a versatile risk management strategy commonly employed by insurers to optimize their risk profile. In this paper, we study an optimal reinsurance design problem minimizing a general law-invariant coherent risk measure of the net risk exposure of a generic insurer, in conjunction with a general law-invariant comonotonic additive convex reinsurance premium principle and a premium budget constraint. Due to its intrinsic generality, this contract design problem encompasses a wide body of optimal reinsurance models commonly encountered in practice. A three-step solution scheme is presented. Firstly, the objective and constraint functions are exhibited in the so-called Kusuoka's integral representations. Secondly, the mini-max theorem for infinite dimensional spaces is applied to interchange the infimum on the space of indemnities and the supremum on the space of probability measures. Thirdly, the recently developed Neyman–Pearson methodology due to Lo (2017a) is adopted to solve the resulting infimum problem. Analytic and transparent expressions for the optimal reinsurance policy are provided, followed by illustrative examples.

Original languageEnglish (US)
Pages (from-to)729-751
Number of pages23
JournalScandinavian Actuarial Journal
Issue number9
StatePublished - Oct 21 2019


  • Budget constraint
  • Neyman–Pearson
  • TVaR
  • distortion
  • mini-max theorem

ASJC Scopus subject areas

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


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