Insurance losses due to flooding can be estimated by simulating and then summing a large number of losses for each in a large set of hypothetical years of flood events. Replicated realisations lead to Monte Carlo return-level estimates and associated uncertainty. The procedure, however, is highly computationally intensive. We develop and use a new, Bennett-like concentration inequality to provide conservative but relatively accurate estimates of return levels. Bennett's inequality accounts for the different variances of each of the variables in a sum but uses a uniform upper bound on their support. Motivated by the variability in the total insured value of risks within a portfolio, we incorporate both individual upper bounds and variances and obtain tractable concentration bounds. Simulation studies and application to a representative portfolio demonstrate a substantial tightening compared with Bennett's bound. We then develop an importance-sampling procedure that repeatedly samples the loss for each year from the distribution implied by the concentration inequality, leading to conservative estimates of the return levels and their uncertainty using orders of magnitude less computation. This enables a simulation study of the sensitivity of the predictions to perturbations in quantities that are usually assumed fixed and known but, in truth, are not.

翻译：洪水保险损失可通过模拟大量假设洪水事件年份中每个事件的损失并进行加总来估算。重复实现过程会产生蒙特卡洛重现期水位估计及其相关不确定性。然而，该计算过程计算量极大。我们开发并运用一种新型的类Bennett集中不等式，以提供保守且相对准确的重现期水位估计。Bennett不等式考虑了求和中各变量的不同方差，但对其支撑集使用了统一上界。受保险组合内风险总投保价值可变性的启发，我们同时纳入个体上界和方差，从而获得可处理的集中界。模拟研究及在代表性保险组合中的应用表明，相较于Bennett界，该方法实现了显著收紧。随后我们开发了一种重要性抽样程序，该程序依据集中不等式隐含的分布对每年的损失进行重复抽样，从而以降低数个数量级的计算量获得重现期水位及其不确定性的保守估计。这使得我们能够通过模拟研究，分析预测结果对通常被假定为固定已知（实则不然）的参数扰动的敏感性。