Diffusion approximation and optimal investment for dependent classes of business

To derive the diffusion approximation of a multi-insurance risk model with dependence introduced by common shocks,and to study the problem of optimal investment,in the case of three for example.Firstly,by model transforming,it is showed that the given dependent risk model can be approximated by a Brownian motion with drift,and thus the approximate distribution of the aggregated claim is obtained.Then,according to the resulted distribution,the optimal investment problem of maximizing the expected terminal wealth is studied,under the constraint of CVaR which measures the integrated risks consisting of claim risks and investment risks and the constraint of supervision of insurance investment.The explicit expressions of optimal strategies are derived by the constrained maximization principle.It is expected to provide some references for an insurer to estimate and control risks in the context of insurance diversification and association.