Abstract

This presentation introduces some recent research work on the optimization problems for the risk models with or without dependence structure. We study the optimal reinsurance strategy in a risk model with m(≥ 2) dependent classes of insurance business, where the claim number processes are correlated through a common shock component or thinning structure. Under the criterion of maximizing the expected utility or minimizing the probability of drawdown, the closed-form expressions for the optimal results are derived for the compound Poisson risk model and (or) for the Brownian motion risk model; We also consider the optimal portfolio problems, where the two risky asset price processes or the risky asset price process and aggregate claim process are correlated through a common shock. Within the mean-variance framework, using the technique of stochastic control theory and the corresponding (extended) Hamilton-Jacobi-Bellman equation, the closed-form expressions of the optimal strategies and value function are obtained. Recently, under the criterion of minimizing the probability of drawdown or minimizing the probability of absolute ruin, some other optimization problems with combined mean-variance premium principle and general reinsurance form are discussed, and some explicit optimal results are given as well.