Dynamic mean-variance problem with constrained risk control for the insurers

In this paper, we study optimal reinsurance/new business and investment (no-shorting) strategy for the mean-variance problem in two risk models: a classical risk model and a diffusion model. The problem is firstly reduced to a stochastic linear-quadratic (LQ) control problem with constraints. Then, the efficient frontiers and efficient strategies are derived explicitly by a verification theorem with the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations, which is different from that given in Zhou et al. (SIAM J Control Optim 35:243-253, 1997). Furthermore, by comparisons, we find that they are identical under the two risk models.