Après les exposés des dernières séances, l’examen du cours MAT8595, Copules et Valeurs Extrêmes avait lieu hier matin. L’énoncé est en ligne, et j’ai aussi écrit quelques éléments de correction, là. En cas de désaccord, m...
Après les exposés des dernières séances, l’examen du cours MAT8595, Copules et Valeurs Extrêmes avait lieu hier matin. L’énoncé est en ligne, et j’ai aussi écrit quelques éléments de correction, là. En cas de désaccord, m...
![Advances in scalable Bayesian computation [day #4]](http://xianblog.files.wordpress.com/2012/03/dscn2538.jpg?w=450&h=253)
Final day of our workshop Advances in Scalable Bayesian Computation already, since tomorrow morning is an open research time ½ day! Another “perfect day in paradise”, with the Banff Centre campus covered by a fine snow blanket, still falling…, and making work in an office of BIRS a dream-like moment. Still looking for a daily theme, […]
We’ve seen Monday, in the MAT8595 course how to use the Generalized Pareto Distribution to estimate some downside risk measures, given a sample (assumed to be i.i.d., I will not mention here properties on extremes for stochastic processes) with distribution . The cumulative distribution function of the Pareto distribution is here For some threshold , and , we can write From Pickands–Balkema–de Haan theorem, if is large enough, then Given our…
In the MAT8595 course, we’ve seen yesterday Hill estimator of the tail index. To be more specific, we did see see that if , with , then Hill estimators for are given by for . Then we did say that satisfies some consistency in the sense that if , but not too fast, i.e. (under additional assumptions on the rate of convergence, it is possible to prove that ). Further,…
Last week, we had a discussion with some colleagues about the fact that – in order to prepare for the SOA exams – we did not have time (so far) to mention results on extreme values in our actuarial program. I did gave an introduction in my nonlife actuarial models class, but it was only an introduction, in three hours, in order to illustrate reinsurance pricing. And I told my…
During the course, we have seen that it is natural to assume that not only the individual claims frequency can be explained by some covariates, but individual costs too. Of course, appropriate families should be considered to model the distribution of the cost , given some covariates .Here is the dataset we’ll use, > sinistre=read.table("http://freakonometrics.free.fr/sinistreACT2040.txt", + header=TRUE,sep=";") > sinistres=sinistre[sinistre$garantie=="1RC",] > sinistres=sinistres[sinistres$cout>0,] > contrat=read.table("http://freakonometrics.free.fr/contractACT2040.txt", + header=TRUE,sep=";") > couts=merge(sinistres,contrat) > tail(couts) nocontrat…
