Abstract
This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton-Jacobi-Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.
| Original language | English |
|---|---|
| Pages (from-to) | 1-22 |
| Number of pages | 22 |
| Journal | RAIRO - Operations Research |
| Volume | 56 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2022 |
Keywords
- Common shock
- Equilibrium strategy
- Mean-variance criterion
- Optimal reinsurance-investment
- Premium principles