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 language | English |
|---|---|
| Pages (from-to) | 81-88 |
| Number of pages | 8 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Aug 2009 |
| Externally published | Yes |
Keywords
- Exponential utility
- HJBI equations
- Model uncertainty
- Optimal investment
- Penalty of ruin
- Proportional reinsurance
- Stochastic differential game