Optimal reinsurance under dynamic VaR constraint

Nan Zhang, Zhuo Jin, Shuanming Li*, Ping Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


This paper deals with the optimal reinsurance strategy from an insurer's point of view. Our objective is to find the optimal policy that maximises the insurer's survival probability. To meet the requirement of regulators and provide a tool to risk management, we introduce the dynamic version of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and worst-case CVaR (wcCVaR) constraints in diffusion model and the risk measure limit is proportional to company's surplus in hand. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. Applying dynamic programming technique, we obtain closed form expressions of the optimal reinsurance strategies and corresponding survival probabilities under both proportional and excess-of-loss reinsurance. Several numerical examples are provided to illustrate the impact caused by dynamic VaR/CVaR/wcCVaR limit in both types of reinsurance policy.

Original languageEnglish
Pages (from-to)232-243
Number of pages12
JournalInsurance: Mathematics and Economics
Publication statusPublished - 1 Nov 2016
Externally publishedYes


  • Conditional Value-at-Risk (CVaR)
  • Dynamic Value-at-Risk (VaR)
  • HJB equation
  • Survival probability
  • Worst-case CVaR (wcCVaR)


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