Risk assessment using suprema data

Christophette Blanchet-Scalliet (1) , Diana Dorobantu (2) , Laura Gay (1) , Véronique Maume-Deschamps (1) , Pierre Ribereau (1)

1 ICJ - Institut Camille Jordan
2 SAF - Laboratoire de Sciences Actuarielle et Financière

The dynamic of temperatures can be modelled by a mean-reverting process such as an Ornstein-Uhlenbeck one. In this study, we estimate the parameters of this process thanks to daily observed suprema of temperatures, which are the only data gathered by some weather stations. The expression of the cumulative distribution function of the process supremum is obtained. The parameters are estimated by a least square method quantiles based on this function. Theoretical results, including mixing property and consistency of model parameter estimation, are provided. The parameters estimation will allow us to estimate risk measures, such as the probability of heat wave. Numerical illustrations are given on simulated data and real ones.

Mots clés: parameters estimation; heat wave risk assessment; supremum law; Ornstein-Uhlenbeck process

Domaines: Probabilités [math.PR]

Christophette Blanchet-Scalliet, Diana Dorobantu, Laura Gay, Véronique Maume-Deschamps, Pierre Ribereau. Risk assessment using suprema data. 2017. ⟨hal-01615196v1⟩