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.
Highlights
The study of an insurer’s optimal reinsurance-investment problem has attracted a lot of attention in the literature of actuarial science in the past few years
Li et al [15] studied an insurer’s reinsurance problem under a mean-variance criterion. They showed that excess-of-loss was the equilibrium reinsurance strategy under a spectrally negative Levy insurance model when the reinsurance premium was computed according to the expected value premium principle
We firstly prove that the optimal reinsurance contract is a proportional reinsurance under the variance premium principle, and the optimal reinsurance contract is an excessof-loss reinsurance under the expected value premium principle
Summary
The study of an insurer’s optimal reinsurance-investment problem has attracted a lot of attention in the literature of actuarial science in the past few years. Zhang et al [34] analyzed the optimal reinsurance strategy for insurers with a generalized mean-variance premium principle They derived the form of optimal reinsurance under the criteria of maximizing the expected utility function of terminal wealth and minimizing the probability of ruin. Li et al [15] studied an insurer’s reinsurance problem under a mean-variance criterion They showed that excess-of-loss was the equilibrium reinsurance strategy under a spectrally negative Levy insurance model when the reinsurance premium was computed according to the expected value premium principle. These papers motivate us to consider the optimal reinsurance forms in.
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