Yesterday, I was uploading some old posts to complete the migration (I get back to my old posts, one by one, to check links of pictures, reformating R codes, etc). And I re-discovered a post published amost 2 years ago, on nuns and Hell’s Angels in an airplaine. It reminded ... [Read more...]

Next Friday, I will give in Montréal a crash course entitled Econometric Modeling in Finance and Insurance with the R Language. Since IFM2 wanted this course to be an opportunity to discover R, the first part o fthe course will be on the R language. Slides can be downloaded ... [Read more...]

(see John Wilkins’ article on the – interesting – history of that phrase http://scienceblogs.com/evolvingthoughts/…). We will see, this week in class, several smoothing techniques, for insurance ratemaking. As a starting point, assume that we do not want to use segmentation techniques: everyone will pay exactly the same price. no ... [Read more...]

Consider the following time series, What does it look like ? I know, this is a stupid game, but I keep using it in my time series courses. It does look like a random walk, doesn’t it ? If we use Philipps-Perron test, yes, it does, __ PP.test(x) Phillips-Perron Unit ... [Read more...]

In actuarial science, and insurance ratemaking, taking into account the exposure can be a nightmare (in datasets, some clients have been here for a few years – we call that exposure – while others have been here for a few months, or weeks). Somehow, simple results because more complicated to compute just ... [Read more...]

This morning, Stéphane asked me tricky question about extracting coefficients from a regression with categorical explanatory variates. More precisely, he asked me if it was possible to store the coefficients in a nice table, with information on the variable and the modality (those two information being in two different ... [Read more...]

In insurance, the law of large numbers (named loi des grands nombres initially by Siméon Poisson, see e.g. http://en.wikipedia.org/…) is usually mentioned to legitimate large portfolios, because of pooling and diversification: the larger the pool, the more ‘predictable’ the losses will be (in a given ... [Read more...]

In order to illustrate the construction of regression tree (using the CART methodology), consider the following simulated dataset, __ set.seed(1) __ n=200 __ X1=runif(n) __ X2=runif(n) __ P=.8*(X1.7) __ Y=rbinom(n,size=1,P) __ B=data.frame(Y,X1,X2) with one dichotomos varible (the variable of interest, ), and two ... [Read more...]

As mentioned in the Appendix of Modern Actuarial Risk Theory, “R (and S) is the ‘lingua franca’ of data analysis and statistical computing, used in academia, climate research, computer science, bioinformatics, pharmaceutical industry, customer analytics, data mining, finance and by some insurers. Apart from being stable, fast, always up-to-date and ... [Read more...]

Following my previous post, a few more things. As mentioned by Frédéric, it is – indeed – possible to compute the probability of all pairs. More precisely, all pairs are not as likely to occur: some teams can play against (almost) eveyone, while others cannot. From the previous table, it ... [Read more...]

Ok, I was supposed to take a break, but Frédéric, professor in Tours, came back to me this morning with a tickling question. He asked me what were the odds that the Champions League draw produces exactly the same pairings from the practice draw, and the official one (... [Read more...]

A few days ago, a former student of mine, David, contacted me about Box-Cox tests in linear models. It made me look more carefully at the test, and I do not understand what is computed, to be honest. Let us start with something simple, like a linea... [Read more...]

(bis repetita) Consider the following regression summary,Call: lm(formula = y1 ~ x1)   Coefficients: Estimate Std. Error t value Pr(__|t|) (Intercept) 3.0001 1.1247 2.667 0.02573 * x1 0.5001 0.1179 4.241 0.00217 **... [Read more...]

A few years ago, I went to listen to Roger Nelsen who was giving a talk about copulas with fractal support. Roger is amazing when he gives a talk (I am also a huge fan of his books, and articles), and I really wanted to play with that concept ... [Read more...]

Yesterday, I was asked how to write a code to generate a compound Poisson variables, i.e. a series of random variables  where  is a counting random variable (here Poisson disributed) and where the 's are i.i.d (and ind... [Read more...]

For the last course MAT8886 of this (long) winter session, on copulas (and extremes), we will discuss risk aggregation. The course will be mainly on the problem of bounding  the distribution (or some risk measure, say the Value-at-Risk) for two random variables with given marginal distribution. For instance, we have ... [Read more...]

Consider our loss-ALAE dataset, and - as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, __ library(evd) __ data(lossalae) __ Z=lossalae __ X=Z[,1];Y=Z[,2] ... [Read more...]

Following the course of this afternoon, I will just upload some codes to make interactive 3d plots, in R. __ library(rgl) __ library(evd); __ data(lossalae) __ U=rank(lossalae[,1]+rnorm(nrow(lossalae), + mean=0,sd=.001))/(nrow(lossalae)+1) ... [Read more...]

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE data... [Read more...]

We have seen extreme value copulas in the section where we did consider general families of copulas. In the bivariate case, an extreme value can be writtenwhere is Pickands dependence function, which is a convex function satisfyingObserve that in ... [Read more...]