Extreme values statistics for Markov chains with applications to Finance and Insurance
Patrice Bertail – Professor at MODAL’X, Université Paris-Ouest-Nanterre-La Défense and CREST-INSEE
& Stéphane Clémençon, Charles Tillier – MODAL’X Université Paris X

The purpose of this paper is to review and give some extensions of the pseudo-regenerative method in the framework of extreme values for general markov chains. The proposed methodology consists in splitting up the observed sample path into regeneration data blocks (in the atomic case) or into data blocks drawn from a distribution approximating the regeneration cycle’s distribution, in the general case, when regeneration times cannot be observed. Then, statistical tools (including bootstrap methods) are built over the sequence of maxima, as if these maxima were i.i.d. We prove the validity of the method and apply it to ruin models as well as to some financial time series.

Student from ENSAE and Paris-Dauphine, P. Bertail obtained his PhD in applied Mathematics in 1992. He is a specialist of Bootstrap methods in econometric and statistical contexts. After 10 years at INRA were he also worked on food risks assessments, he became Professor at Paris-X in 2000. Since then his research have focused on extending resampling techniques (Bootstrap, subsampling, empirical likelihood) method for dependent data, especially in the field of risk assessment, including ruin models, extremes.