Approches spatio-temporelles pour la modélisation du risque – AST&Risk

Modeling various risks associated to financial and insurance activities is a required step for the evaluation of induced costs and allows to measure the incidence of risks on the solvency of an insurance company or a financial organism. Models have to take in account many interacting entities (modeled by random variables or stochastic processes) which are time-evoluting (long time models). Most classical models assume some spatial (between variables) or temporal independence. However, in many situations, these hypotheses are not satisfied. Assuming independence in such cases is known to provide wrong estimations of the global risk. Moreover, regulatory rules (such as Basel 2 for banking or Solvency 2 for insurance) are strongly incentive to construct realistic models. If models allowing some types of dependence have been proposed, the spatio-temporal modeling remains unsatisfactory. The goal of our project is therefore to construct models that - are rich enough to provide a reasonable approximation of reality, - are tractable, and may be simulated efficiently, - enjoy nice mathematical properties allowing estimation and forecast. This is an « amont » project with important applications for socio-economics, mainly in finance and insurance. Probabilistic and statistical concepts and tools will be developed (connected with point processes, temporal processes, asymptotic properties ...) which might have an intrinsic interest for mathematicians. This is the reason why we ask for an evaluation of the project by the CSD 5 (Mathématiques et interactions) of the ANR.