In this paper, we determine the optimal reinsurance strategy to minimize the probability of drawdown, namely, the probability that the insurer's surplus process reaches some fixed fraction of its maximum value to date. We assume that the reinsurance premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We derive closed-form expressions of the optimal reinsurance strategy and the corresponding minimum probability of drawdown. Then, under the variance premium principle, we show that the safe level can never be reached before drawdown under the optimally controlled surplus process. Finally, we present some numerical examples to show the impact of model parameters on the optimal results.

中文翻译：

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在均值方差保费原则下最小化回撤概率的最优再保险

在本文中，我们确定了最佳再保险策略以最小化回撤概率，即保险公司的盈余过程达到其迄今为止最大值的某个固定部分的概率。我们假设再保险保费是根据平均方差保费原则计算的，这是期望值和方差保费原则的组合。我们推导出最优再保险策略和相应的最小回撤概率的闭式表达式。然后，在方差溢价原则下，我们证明了在最优控制的盈余过程下，在回撤之前永远不会达到安全水平。最后，我们给出了一些数值例子来说明模型参数对优化结果的影响。