Quantifying the sources of simulation uncertainty in natural catastrophe models

摘要

The risk from natural catastrophes is typically estimated using complex simulation models involving multiple stochastic components in a nested structure. This risk is principally assessed via the mean annual loss, and selected quantiles of the annual loss. Determining an appropriate simulation strategy is important in order to achieve satisfactory convergence of these statistics, without excessive computation time and data storage requirements. This necessitates an understanding of the relative contribution of each of the stochastic components to the total variance of the statistics. A simple framework using random effects models and analysis of variance is used to partition the variance of the annual loss, which permits calculation of the variance of the mean annual loss with varying numbers of samples of each of the components. An extension to quantiles is developed using the empirical distribution function in combination with bootstrapping. The methods are applied to a European flood model, where the primary stochastic component relates to the frequency and severity of flood events, and three secondary components relate to defence levels, exposure locations and building vulnerability. As expected, it is found that the uncertainty due to the secondary components increases as the size of the portfolio of exposures decreases, and is higher for industrial and commercial business, compared with residential for all statistics of interest. In addition, interesting insights are gained as to the impact of flood defences on convergence.