Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no temporal d
ependence. Only a few papers have introduced spatio-temporal max-stable models, extending the Smith, Schlather and Brown-Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role as space and the temporal dynamics is not explicit. In order to overcome these defects, we introduce spatio-temporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous and discrete-tim
The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environme
ntal events into the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms for these spatial risk measures. These axioms quantify the sensitivity of the risk measure with respect to the space and are especially linked to spatial diversification. The proposed model for the cost underlying our definition of spatial risk measure involves applying a damage function to the environmental variable considered. We build and theoretically study concrete examples of spatial risk measures based on the indicator function of max-stable processes exceeding a given threshold. Some interpretations in terms of insurance are provided.
We test the hypothesis that interconnections across financial institutions can be explained by a diversification motive. This idea stems from the empirical evidence of the existence of long-term exposures that cannot be explained by a liquidity motiv
e (maturity or currency mismatch). We model endogenous interconnections of heterogenous financial institutions facing regulatory constraints using a maximization of their expected utility. Both theoretical and simulation-based results are compared to a stylized genuine financial network. The diversification motive appears to plausibly explain interconnections among key players. Using our model, the impact of regulation on interconnections between banks -currently discussed at the Basel Committee on Banking Supervision- is analyzed.
Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a lot of zer
os (dry hours) and they have complex temporal structures (e.g., long persistence of dry episodes). Inspired by frailty-contagion approaches used in finance and insurance, we propose a multi-site precipitation simulator that, given appropriate regional atmospheric variables, can simultaneously handle dry events and heavy rainfall periods. One advantage of our model is its conceptual simplicity in its dynamical structure. In particular, the temporal variability is represented by a common factor based on a few classical atmospheric covariates like temperatures, pressures and others. Our inference approach is tested on simulated data and applied on measurements made in the northern part of French Brittany.
