Optimal risk control for the excess of loss reinsurance policies

Hui Meng*, Xin Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


The primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

Original languageEnglish
Pages (from-to)179-197
Number of pages19
JournalASTIN Bulletin
Issue number1
Publication statusPublished - May 2010


  • Excess of loss
  • Hamilton-Jacobi-Bellman equation
  • Investments
  • Minimal probability of ruin
  • Stochastic control


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