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

Halis Sak*, Guanyu Yang, Bailiang Li, Weifeng Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM2.5 concentration in cities. The model used is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM2.5 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 PM2.5 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 352μgm-3 (initial PM2.5 concentrations of cities are assumed to be 100μgm-3) 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.

Original languageEnglish
Pages (from-to)2607-2616
Number of pages10
JournalStochastic Environmental Research and Risk Assessment
Issue number10
Publication statusPublished - 1 Dec 2017


  • Pollution risk
  • Risk management
  • Stratified importance sampling
  • t-Copula


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