The k-year return levels of insurance losses due to flooding can be estimated by simulating and then summing a large number of independent losses for each of a large number of hypothetical years of flood events, and replicating this a large number of times. This leads to repeated realisations of the total losses over each year in a long sequence of years, from which return levels and their uncertainty can be estimated; the procedure, however, is highly computationally intensive. We develop and use a new, Bennett-like concentration inequality in a procedure that provides conservative but relatively accurate estimates of return levels at a fraction of the computational cost. Bennett's inequality provides concentration bounds on deviations of a sum of independent random variables from its expectation; it accounts for the different variances of each of the variables but uses only a single, uniform upper bound on their support. Motivated by the variability in the total insured value of insurance risks within a portfolio, we consider the case where the bounds on the support can vary by an order of magnitude or more, and obtain tractable concentration bounds. Simulation studies and application to a representative portfolio demonstrate the substantial improvement of our bounds over those obtained through Bennett's inequality. 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.

翻译：洪水保险的k年返回水平可通过模拟假设年份的洪水事件、对每一年大量独立损失求和并重复多次来估计。这一过程需生成长期序列中每年总损失的重复实现值，进而估计返回水平及其不确定性，但计算成本极高。我们提出并应用一种新型类Bennett浓度不等式，在保守前提下以极低计算成本获得相对精确的返回水平估计。Bennett不等式刻画独立随机变量之和偏离其期望的浓度界，虽考虑了各变量的方差差异，但仅使用单一均匀支撑上界。受保险组合中总保额波动性的启发，我们研究了支撑上界可相差数量级甚至更大的情形，推导出易处理的浓度界。仿真实验及代表性组合应用表明，所获界显著优于Bennett不等式结果。进一步，我们基于该浓度不等式隐含分布对每年损失进行重要抽样，实现返回水平及其不确定性的保守估计。