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A copula-based model for air pollution portfolio risk and its efficient simulation

Sak, Halis, Yang, Guanyu, Li, Bailiang, Li, Weifeng
Stochastic environmental research and risk assessment 2017 v.31 no.10 pp. 2607-2616
air pollution, cities, data collection, models, risk, China
This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM[Formula: see text] concentration in cities. The model used is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM[Formula: see text] levels of Beijing, Tianjin, Chengde, Hengshui, and Xingtai. This process reveals a better fit for the t-copula dependence structure with generalized hyperbolic marginal distributions for the PM[Formula: see text] log-ratios of the cities. Furthermore, we show how to efficiently simulate risk measures clean-air-at-risk and conditional clean-air-at-risk using importance sampling and stratified importance sampling. Our numerical results show that clean-air-at-risk at 0.01 probability level reaches up to [Formula: see text] (initial PM[Formula: see text] concentrations of cities are assumed to be [Formula: see text]) for the constructed sample portfolio, and that the proposed methods are much more efficient than a naive simulation for computing the exceeding probabilities and conditional excesses.