Very unhealthy air quality is consistently connected with numerous diseases. Appropriate extreme analysis and accurate predictions are in rising demand for exploring potential linked causes and for providing suggestions for the environmental agency in public policy strategy. This paper aims to model the spatial and temporal pattern of both moderate and extremely poor PM $$_{10}$$10 concentrations (of daily mean) collected from 342 representative monitors distributed throughout mainland Spain from 2017 to 2021. We first propose and compare a series of Bayesian hierarchical generalized extreme models of annual maxima PM $$_{10}$$10 concentrations, including both the fixed effect of altitude, temperature, precipitation, vapour pressure and population density, as well as the spatio-temporal random effect with the Stochastic Partial Differential Equation (SPDE) approach and a lag-one dynamic auto-regressive component (AR(1)). Under WAIC, DIC and other criteria, the best model is selected with good predictive ability based on the first four-year data (2017–2020) for training and the last-year data (2021) for testing. We bring the structure of the best model to establish the joint Bayesian model of annual mean and annual maxima PM $$_{10}$$10 concentrations and provide evidence that certain predictors (precipitation, vapour pressure and population density) influence comparably while the other predictors (altitude and temperature) impact reversely in the different scaled PM $$_{10}$$10 concentrations. The findings are applied to identify the hot-spot regions with poor air quality using excursion functions specified at the grid level. It suggests that the community of Madrid and some sites in northwestern and southern Spain are likely to be exposed to severe air pollution, simultaneously exceeding the warning risk threshold.

Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning.

The constantly expanding losses caused by frequent natural disasters pose many challenges to the traditional catastrophe insurance market. The purpose of this paper is to develop an innovative and systemic trigger mechanism for pricing catastrophic bonds triggered by multiple events with an extreme dependence structure. Due to the bond’s low cashflow contingencies and the CAT bond’s high return, the multiple-event CAT bond may successfully transfer the catastrophe risk to the huge financial markets to meet the diversification of capital allocations for most potential investors. The designed hybrid trigger mechanism helps reduce the moral hazard and increase the bond’s attractiveness with a lower trigger likelihood, displaying the determinants of the wiped-off coupon and principal by both the magnitude and intensity of the natural disaster events involved. As the trigger indicators resulting from the potential catastrophic disaster might be associated with heavy-tailed margins, nested Archimedean copulas are introduced with marginal distributions modeled by a POT-GP distribution for excess data and common parametric models for moderate risks. To illustrate our theoretical pricing framework, we conduct an empirical analysis of pricing a three-event rainstorm CAT bond based on the resulting losses due to rainstorms in China during 2006–2020. Monte Carlo simulations are carried out to analyze the sensitivity of the rainstorm CAT bond price in trigger attachment levels, maturity date, catastrophe intensity, and numbers of trigger indicators.

Climate change increases the risk of illness through rising temperature, severe precipitation and worst air pollution. This paper investigates how monthly excess mortality rate is associated with the increasing frequency and severity of extreme temperature in Canada during 2000-2020. The extreme associations were compared among four age groups across five sub-blocks of Canada based on the datasets of monthly T90 and T10, the two most representative indices of severe weather monitoring measures developed by the actuarial associations in Canada and US. We utilize a combined seasonal Auto-regressive Integrated Moving Average (ARIMA) and bivariate Peaks-Over-Threshold (POT) method to investigate the extreme association via the extreme tail index $$\chi$$χ and Pickands dependence function plots. It turns out that it is likely (more than 10%) to occur with excess mortality if there are unusual low temperature with extreme intensity (all $$\chi >0.1$$χ > 0.1 except Northeast Atlantic (NEA), Northern Plains (NPL) and Northwest Pacific (NWP) for age group 0-44), while extreme frequent high temperature seems not to affect health significantly (all $$\chi \le 0.001$$χ ≤ 0.001 except NWP). Particular attention should be paid to NWP and Central Arctic (CAR) since population health therein is highly associated with both extreme frequent high and low temperatures (both $$\chi =0.3182$$χ = 0.3182 for all age groups). The revealed extreme dependence is expected to help stakeholders avoid significant ramifications with targeted health protection strategies from unexpected consequences of extreme weather events. The novel extremal dependence methodology is promisingly applied in further studies of the interplay between extreme meteorological exposures, social-economic factors and health outcomes.