Optimal reinsurance policies with two reinsurers in continuous time

Hui Meng*, Ming Zhou, Tak Kuen Siu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability.

Original languageEnglish
Pages (from-to)182-195
Number of pages14
JournalEconomic Modelling
Volume59
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Expected value premium principle
  • Variance premium principle
  • Ruin probability
  • Proportional reinsurance
  • Excess of loss reinsurance
  • Dynamic programming principle
  • Heavy-tailed claims
  • RISK CONTROL
  • DIVIDEND DISTRIBUTION
  • PREMIUM PRINCIPLES
  • DIFFUSION-MODEL
  • DEPENDENT RISKS
  • EXCESS

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