Laura Gay - Risk measures in a temperature model

Forecasting and assessing the risk of heat waves is a crucial public policy stake. It requires measure tools in order to evaluate the probability of heat waves and their severity. The available information depends on meteorological stations. Daily extremes (maximum and / or minimum) might be the only available data. We are interested by estimating this dynamic of temperatures in order to evaluate the related risk measures. This dynamic can be modelled by a mean-reverting process such as an Ornstein-Uhlenbeck process. We will first recall previous results about the estimation of the parameters of this process thanks to daily observed suprema of temperatures. This estimation will allow us to estimate risk measures, such as the probability of heat waves. Then, we will talk about obtaining analytical expressions for risk measures using the joint law of the process and its supremum. I will give explanations about how to obtain this joint law.