Optimally stratified importance sampling for portfolio risk with multiple loss thresholds

Tail loss probability is an essential risk measure for linear asset portfolios. The paper presents an efficient simulation algorithm that combines importance sampling and optimal stratification to estimate tail loss probabilities for linear asset portfolios under the t-copula model. Based on the combined method, an efficient procedure is developed for estimating multiple tail loss probabilities in a single simulation. For this purpose, a heuristic determines sample allocation fractions in the strata such that the maximum relative error is minimized. This idea and the heuristic can be used to minimize the maximum relative error of an arbitrary simulation associated with multiple estimates.