Modeling of rare events for risk management

Abstract

Nowadays, risk management plays a key role especially in socio-economic world such as: commerce, industry, agriculture, �nance, insurance, soci- ology, medicine, politics and sport, etc. Hence we need some tools in order to control that risk. So we de�ne theoretical quantities that we call risk measures and we will be able to estimate it appropriately. It is obvious that in order to make a precise estimate, we must �nd the theoretical model most appropriate to the data. This is done using extreme value theory, which seems to be the best tool for modeling rare events that greatly in�uence the behavior of companies to deal with dangerous risks. This study aims to estimate the various parameters of a model of extreme values in order to be able to approach the estimation of the risk measures. Those results will be applied especially in extreme hydrological events such as �oods, which are one of the natural disasters that occur in several parts of the world. They are regarded as being the most costly natural risks in terms of the disastrous consequences in human lives and in property damages. The main objective of the present study is to estimate �ood events of Abiod wadi at given return periods at the gauge station of M�chouneche, located closely to the city of Biskra in a semiarid region of southern east of Algeria. This is a problematic issue in several ways, because of the existence of a dam to the downstream, including the �eld of the sedimentation and the water leaks through the dam during �oods. A complete frequency analysis is performed on a series of observed daily aver- age discharges, including classical statistical tools as well as recent techniques. The obtained results show that the generalized Pareto distribution (GPD), for which the parameters were estimated by the maximum likelihood (ML) method, describes the analyzed series better. This study also indicates to the decision- makers the importance to continue monitoring data at this station.