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In this paper we study a mean-variance portfolio selection problem with stopping time in two risk models: a classical risk model and a jump-diffusion model.The stopping time is defined by which the insurerss surplus first falls below a preselect level.The optimal portfolio,reinsurance strategy and corresponding efficient frontier in closed form are derived by using the stochastic linear-quadratic(LQ) control theory and viscosity solution theory.Finally,the distribution of the stopping time is obtained by Laplace transform.Furthermore,these results are illustrated by a numerical example.