Optimal investment and reinsurance of an insurer with model uncertainty

Xin Zhang, Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)

Abstract

We introduce a novel approach to optimal investment-reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment-reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton-Jacobi-Bellman-Isaacs (HJBI) solutions to the optimal investment-reinsurance problems and derive closed-form solutions to the problems.

Original languageEnglish
Pages (from-to)81-88
Number of pages8
JournalInsurance: Mathematics and Economics
Volume45
Issue number1
DOIs
Publication statusPublished - Aug 2009
Externally publishedYes

Keywords

  • Exponential utility
  • HJBI equations
  • Model uncertainty
  • Optimal investment
  • Penalty of ruin
  • Proportional reinsurance
  • Stochastic differential game

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