均值-方差保费原则下最小化提取概率的最优再保险：渐近分析
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis
摘要：
本文考虑了在按均值-方差原则计算再保险费的情况下，比例Cramér-Lundberg风险模型的最优再保险问题.我们将Liang等人的工作扩展到最小化提款概率的情况。[16]。利用比较方法和调整系数工具，证明了比例经典风险模型的最小缩编概率收敛于其扩散近似的最小缩编概率，且收敛速率为$O(n^{-1/2})$阶.我们进一步证明了在标度经典风险模型中使用来自扩散近似的最优策略是$O(n^{-1/2})$ -最优的。
英文摘要：
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cramér-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang et al. [16] to the case of minimizing the probability of drawdown. By using the comparison method and the tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled classical risk model converges to the minimum probability for its diffusion approximation, and the rate of convergence is of order $O(n^{-1/2})$. We further show that using the optimal strategy from the diffusion approximation in the scaled classical risk model is $O(n^{-1/2})$-optimal.
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