# Multivariate and dynamic risk measures

After a few years, I decided to put online some lectures notes I had from a graduate course I gave over one (long) day in 2014, in Leuven, entitled “an introduction to multivariate and dynamic risk measures”. The notes are now available on hal. I just hope that it might be usefull to someone…

# Earthquake dynamics

I just upload on http://hal.archives-ouvertes.fr/hal-00871883 a joint paper entitled Modeling earthquake dynamics.

In this paper, we investigate questions arising in Parsons & Geist (2012). Pseudo causal models connecting magnitudes and waiting times are consider, through generalized regression. We do use conditional model (magnitude given previous waiting time, and conversely) as an extension to joint distribution model described in Nikoloulopoulos & Karlis (2008). On the one hand, we fit a Pareto distribution for earthquake magnitudes, where the tail index is a function of waiting time following previous earthquake; on the other hand, waiting times are modeled using a Gamma or a Weibull distribution, where parameters are function of the magnitude of the previous earthquake. We use those two models, alternatively, to generate the dynamics of earthquake occurrence, and to estimate the probability of occurrence of several earthquakes within a year, or a decade.

# Basketball: score dynamics and game theory

Tomorrow morning, I will be giving a talk at Mont Tremblant, for the Journées de la Société Canadienne de Sciences Economiques. I will present a joint work – in progress – with Nathalie Colombier and Romuald Elie. Since the working paper is not online yet, I will wait a little bit before uploading the slides. But they will be online, someday (hopefully soon)…

An important aspect of the strategy of most organizations is the provision of incentives to the employees to meet the organization’s objectives. Typically this implies tying pay to performance (see Prendergast, 1999). In order to reward employees for their effort, ﬁrms spend considerable resources on performance evaluations. In many cases, evaluation consists of comparing actual performance to a pre-deﬁned individual target. Another frequently used format is relative performance evaluation. Relative performance evaluation may motivate employees to work harder.But it may also be demoralizing and create an excessively competitive workplace, which may hinder overall performance; see Lazear (1989). Determining the overall impact of relative performance evaluation is crucial for companies. Economic research on relative performance evaluation has mainly focused on the comparison of ﬁnal performances between competitors,like in tournament theory, and on quantitative and subjective performance ratings (Lazear and Gibbs, 2009). In contrast, what happens during a competition and the impact of feedback frequency on effort have so far received little attention. Following Berger and Pope (2011), we decided to use a basketball application to get a better understanding of the role of the feedback information. Sports datasets allow to observe score and team behavior continuously (during a game but also during the season) which can be use as a proxy of the effort. Berger an Pope (2010) asked ”can loosing lead to winning ?” looking at the impact of the halftime score difference on winning probability in NCAA (college) and NBA(pro) games. More precisely, they studied whether a team loosing at halftime is more likely to win than expected using a logit model. They ﬁnd that usually the higher the score difference the more likely the are to win. But if the halftime score difference is around 0 they observe a discontinuity: loosing with a small difference (e.g. down by 1 point) can lead to increase the effort and win the game. In this paper we try answer the question ”when loosing lead to winning ?”.

# Dynamic dependence ordering for Archimedean copulas and distorted copulas

The paper on Dynamic dependence ordering for Archimedean copulas and distorted copulas should appear soon in Kybernetika.

This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i.e. given remaining lifetimes X, to compare the dependence of X given X>t, and X given X>s, where s>t. More precisely, analytical results will be obtained in the case the survival copula of X is either Archimedean or a distorted copula. The case of a frailty based model will also be discussed in details.