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The k-year return levels of insurance losses due to flooding can be estimatedby simulating and then summing a large number of independent losses for each ofa large number of hypothetical years of flood events, and replicating this alarge number of times. This leads to repeated realisations of the total lossesover each year in a long sequence of years, from which return levels and theiruncertainty can be estimated; the procedure, however, is highly computationallyintensive. We develop and use a new, Bennett-like concentration inequality in aprocedure that provides conservative but relatively accurate estimates ofreturn levels at a fraction of the computational cost. Bennett's inequalityprovides concentration bounds on deviations of a sum of independent randomvariables from its expectation; it accounts for the different variances of eachof the variables but uses only a single, uniform upper bound on their support.Motivated by the variability in the total insured value of insurance riskswithin a portfolio, we consider the case where the bounds on the support canvary by an order of magnitude or more, and obtain tractable concentrationbounds. Simulation studies and application to a representative portfoliodemonstrate the substantial improvement of our bounds over those obtainedthrough Bennett's inequality. We then develop an importance sampling procedurethat repeatedly samples the loss for each year from the distribution implied bythe concentration inequality, leading to conservative estimates of the returnlevels and their uncertainty.

Fast return-level estimates for flood insurance via an improved Bennett inequality for random variables with differing upper bounds