All posts by Arthur Charpentier

Arthur Charpentier, professor in Montréal, in Actuarial Science. Former professor-assistant at ENSAE Paristech, associate professor at Ecole Polytechnique and assistant professor in Economics at Université de Rennes 1.  Graduated from ENSAE, Master in Mathematical Economics (Paris Dauphine), PhD in Mathematics (KU Leuven), and Fellow of the French Institute of Actuaries.

Exposé à Toulouse sur l’estimation (nonparamétrique) de quantiles

Exposé à Toulouse 1, sur l’estimation nonparamétrique de quantiles.

In this talk we propose several nonparametric estimators of quantiles based on Beta kernel and applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte-Carlo based study will show that those estimators improve the efficiency, not only for light tailed distributions, but mainly for heavy tailed, when the probability level is close to 1. Another application will be seen, on portfolio optimization in the mean-VaR context.

Dynamic flood modeling: combining Hurst and Gumbel’s approach

The paper (with David Sibai) on High Frequency models in hydrology just appeared, in Environmetrics.

When working on river floods—annual river levels maxima—, two approaches are usually considered: one inspired from Emil Gumbel where annual maxima are supposed to be i.i.d. and distributed according to Gumbel’s distribution, and one inspired from Edwin Hurst where annual maxima are strongly dependent, and exhibit long range memory. This paper tries to solve this apparent paradox by deriving a dynamic model inspired from financial models, which does not take into account annual maxima only but also threshold exceedances. It studies the implications of such a paradox in terms of return period—a notion valid as long as the data are i.i.d—and of extremal events.

Sales forecasting

Quelques heures de cours à l’ESC Rennes sur sur le thème Sales Forecasting. Les slides sont en ligne, avec la partie 1 et la partie 2 (j’ai aussi mis en ligne la base de données sur le trafic autoroutier). Parmi les contraintes techniques, il fallait utiliser Excel (exclusivement). Je mets donc des liens vers macro1 et macro2 qui sont des add-ins permettant de faire un peu de séries temporelles. Sinon un petit exemple est aussi disponible…

La partie 1 est

et la partie 2

Advances in copula density estimation

Exposé aux Gemeinsame Jahrestagung der Deutschen Mathematiker-Vereinigung und der Gesellschaft für Didaktik der Mathematik, dans la session Multivariate Dependence Modelling using Copulas – Applications in Finance, Humboldt-Universität zu Berlin, Mars 2007, à partir du chapitre écrit avec Jean David Fermanian et Olivier Scaillet sur The estimation of copulas : theory and pratice.

Copulas are a way of formalising dependence structures of random vectors. Although they have been known about for a long time (Sklar (1959)), they have been rediscovered relatively recently in applied sciences (biostatistics, reliability, biology, etc). In finance, they have become a standard tool with broad applications: multiasset pricing (especially complex credit derivatives), credit portfolio modelling, risk management, etc. For example, see Li (1999), Patton (2001) and Longin and Solnik (1995). […] In this chapter, we focus on the practical issues practitioners are faced with, in particular concerning estimation and visualisation. In the first section, we give a general setting for the estimation of copulas. Such a framework embraces most of the available techniques. In the second section, we deal with the estimation of the copula density itself, with a particular focus on estimation near the boundaries of the unit square.