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In this paper, we consider an optimal reinsurance problem to minimize theprobability of drawdown for the scaled Cram\'er-Lundberg risk model when thereinsurance premium is computed according to the mean-variance premiumprinciple. We extend the work of Liang et al. [16] to the case of minimizingthe probability of drawdown. By using the comparison method and the tool ofadjustment coefficients, we show that the minimum probability of drawdown forthe scaled classical risk model converges to the minimum probability for itsdiffusion approximation, and the rate of convergence is of order $O(n^{-1/2})$.We further show that using the optimal strategy from the diffusionapproximation in the scaled classical risk model is $O(n^{-1/2})$-optimal.

Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis