🤖 AI Summary
Monte Carlo estimation of return periods in flood insurance incurs prohibitively high computational costs. Method: This paper proposes an enhanced Bennett-type concentration inequality that jointly incorporates heterogeneous upper bounds and variances of random variables, integrated with importance sampling. It is the first to jointly model individual upper bounds and variances within the Bennett framework, yielding tighter, more conservative, and computationally tractable theoretical bounds on the tail of the annual loss distribution. Contribution/Results: The method reduces computational effort for return period estimation by several orders of magnitude. When applied to real-world insurance portfolios, it substantially tightens bounds compared to standard approaches. Moreover, it enables rapid sensitivity analysis of key modeling assumptions—such as loss distribution parameters and dependence structures—while preserving theoretical rigor and practical deployability in actuarial and risk management applications.
📝 Abstract
Insurance losses due to flooding can be estimated by simulating and then summing losses over a large number of locations and 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 annual losses from the distributions implied by each year's 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.
