Direct calculation of the probability distribution for earthquake losses to a portfolio

We demonstrate a direct method for the calculation of the annual frequency of exceedance for earthquake losses (or the probability distribution for annual losses) to a portfolio. This method parallels the classic method of probabilistic seismic hazard analysis for the calculation of the annual frequency of exceedance for earthquake ground motions. The method assumes conditional independence of the random component of ground motions and losses at different sites for each earthquake, given magnitude, distance to the sites, and so-called interevent epsilon. Examples show that the method is realizable, and can take into account different loss functions and site conditions in the portfolio. The main advantage of this method is that it does not require a separate set of scenario earthquakes, as do Monte Carlo-based approaches, but can be calculated directly from the inputs used for hazard maps.