In this paper, we consider an optimal proportional reinsurance problem for the compound Poisson risk model with delay and multiple dependent classes of insurance business. Under the criterion of maxi-mizing the mean-variance utility of the terminal wealth, we formulate the time-inconsistent problem within a game theoretic framework and look for a subgame perfect Nash equilibrium strategy. Based on the technique of stochastic control theory and the corresponding extend-ed Hamilton-Jacobi-Bellman equation, the explicit expressions of the optimal equilibrium strategy and the value function are derived for the case of insurance business n = 2. Meanwhile, we derive the closed-form expressions of optimal solutions for the case of n = 3 by the method of dimension reduction which can be used to get the op-timal results for the case of n > 3. Finally, some numerical examples are presented to show the impact of model parameters on the optimal strategies. |