Category Archives: Trip

Chicago, Baseball and Paul Erdös

Thursday afternoon, before the 2013 CAE Faculty Conference, Stuart Klugman should invit us to go and watch the Cubs playing, in Chicago. That should be fun. First baseball game, ever. I will be back in Montréal (and on the blog) next week !

That will be an opportunity to discuss with mathematicians and baseball fans. Actually, a colleague told me that there was a nice anecdote about baseball and mathematics. Hank Aaron, “considered to be one of the greatest baseball players of all time” is supposed to have an Erdös number of 1 (see e.g. http://boolesrings.org/mpawliuk/….). Some pretend that it is only because Hank Aaron has signed the same baseball as Paul Erdös (thus, they cosigned something, giving him the Erdös number 1) while both of them were invited in some ceremony to get honorary diplomas… The funny part is that, even if he was not a mathematician (but has an Erdös number of 1), he also has named some numbers, the so-called Ruth–Aaron pairs. The story is nice, actually. On April 1974, Hank Aaron become famous for swatting his 715th home run. The prior record was held by Babe Ruth, with (have a wise guess…) 714 home run. Three mathematicians in Georgia (including Carl Pomerance) notice that 714 × 715 was not a common pair of consecutive number. It consists of two consecutive integers for which the sums of the prime factors of each integer are equal, since

714 = 2 × 3 × 7 × 17

715 = 5 × 11 × 13

and

2 + 3 + 7 + 17 = 5 + 11 + 13    (= 29)

Those are Ruth-Aaron pairs, see e.g. http://mathworld.wolfram.com/… or Pomerance (1999). Note that Carl Pomerance published more than 40 papers with Paul Erdös. End of the loop.

Amsterdam, PhD defense

http://freakonometrics.hypotheses.org/files/2013/01/Capture-d%E2%80%99e%CC%81cran-2013-01-21-a%CC%80-09.14.31.png

Last week, I was involved in the PhD defense of Julien Tomas, with Rob Kaas (promotor), Frédéric Planchet (co-promotor), Katrien AntonioMarc Goovaerts, Ann De Schepper and Michel Vellekoop. The PhD thesis – untitled quantifying biometric life insurance risks with non-parametric smoothing methods – can be dowloaded on http://dare.uva.nl/… and on http://tel.archives-ouvertes.fr/.

http://freakonometrics.hypotheses.org/files/2013/01/Capture-d%E2%80%99e%CC%81cran-2013-01-21-a%CC%80-09.13.07.png

The R codes will be available soon on my blog (and on Julien’s new website http://www.likelihood.me/).

http://freakonometrics.hypotheses.org/files/2013/01/Capture-d%E2%80%99e%CC%81cran-2013-01-21-a%CC%80-09.13.29.png http://freakonometrics.hypotheses.org/files/2013/01/Capture-d%E2%80%99e%CC%81cran-2013-01-21-a%CC%80-09.15.01.png http://freakonometrics.hypotheses.org/files/2013/01/Capture-d%E2%80%99e%CC%81cran-2013-01-21-a%CC%80-09.13.45.png

Amsterdam

I will be in Amsterdam for the end of this week. I will be in the jury of the PhD defense of Julien Tomas, entitled “Quantifying Biometric Life Insurance Risks With Non-Parametric Smoothing Methods” (the thesis will probably be online soon). But before, I will give a talk at the actuarial seminar at UvA. My visit last time was a real pleasure, and it should be the same this time too. I will give a talk this Thursday on “R for actuarial science“. The slides can be downloaded from here.

Pricing catastrophe options in incomplete markets

The paper on the pricing of catastrophe options just appeared in the Proceedings of the Actuarial and Financial Mathematics Conference.

In complete markets, pricing financial products is easy (at least from a theoretical point of view). In incomplete markets (e.g. when the underlying process has jumps with random size, such as an insurance loss process), the price is no longer unique. So on the one hand, it becomes difficult to provide a tractable price of insurance-linked derivatives. On the other hand, when facing catastrophic losses, using the pure premium as a price might not be relevant (e.g. for solvency issues). Both financial market and (re)insurance industry have proposed techniques to price identical hedging products that can be related (e.g. Esscher transform and more generally distorted risk measures in insurance, Gerber-Shiu transform in finance). In this paper, we focus on indifference utility techniques, assuming that stock prices have jumps,related to major catastrophic losses, and thus, partial hedging should then be possible.

La conférence cette année se tiendra les 5 et 6 février (site) a Bruxelles.

 

Journées de statistiques, Ottawa

Je serais aux Journées de Statistiques, a Ottawa, avec au programme un exposé sur Tails of Archimedean copulas.

Un répertoire complet et convivial des queues de copules est présenté. Il peut être utilisé pour la sélection et la construction de modèles appropriés avec les propriétés voulues. Les résultats sont synthétisés sous forme d’arbre de décision : compte tenu des valeurs de certaines caractéristiques du générateur archimédien, chacune des queues inférieures et supérieures de la copule est classée dans une des trois catégories, l’une de ces catégories correspondant à la dépendance asymptotique et les deux autres à l’indépendance asymptotique. Pour une longue liste de familles à paramètre unique, les quantités pertinentes de queues sont calculées afin que les catégories correspondantes dans l’arbre de décision puissent être facilement déterminées. De plus, de nouveaux modèles avec des queues inférieures et supérieures personnalisées peuvent être créés grâce à un certain nombre de méthodes de transformation. On constate que la catégorie de l’indépendance asymptotique, qui se présente souvent, masque une  diversité étonnamment riche de structures de dépendance de queue.

Je serais aussi organisateur de la session Copules, avec comme invités Anne Catherine Favre (site), Johanna Neslehova (site), et Stéphane Loisel (site).

Pricing catastrophe options in incomplete markets

Exposé sur Pricing catastrophe options in incomplete markets, à la conférence Actuarial and Financial Mathematics Conference (interplay between Finance and Insurance), à Bruxelles.

Cet exposé présentait la problématique de la valorisation d’options sur indices catastrophes (en marché incomplets). Une version détaillée apparaîtra dans les Proceedings.

Talk on Value-at-Risk estimation

Exposé au séminaire d’Actuariat, à la faculté de Sciences Economiques à Amsterdam (UvA). L’exposé portera sur l’estimation de quantiles (et de Value-at-Risk) sur des données de pertes, avec une application de gestion de portefeuille moyenne-VaR.

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.

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.