We are flying, this morning for three weeks in the National Parks, in the western part of the United states. First stop, Las Vegas, as mentioned in a couple of posts already. I did mention in a post in April that I did plan to visit the casinos, but more to see people gambling. And in that post, I noticed that if you play the roulette, and if your plan is to double your gain, then you’d better play big. And bet everything once. Actually, it did happen a few years ago, as a friend recently told me. Ashley Revell, 32 by that time, literally sold every that he had owned to bet on the roulette table (in Vegas). The total of his possessions came to £76,840, which gave him around $135,300 in total to bet with on one spin of the roulette wheel. And he did play everything. Ashley pushed his chips on red, the ball bobbled around the wheel, and it finally came to rest in the 7 Red slot, doubling his winnings to $270,600. But actually, as Ashley explained, it was surprisingly difficult to find a Casino in Vegas to take up such a large bet (most of them simply refused to host to such a big gamble). But a TV show decided to record the bet, and the high stakes bet was finally taken up by the casino at Plaza Hotel.
But I do not plan to play everything I own. And I really want to enjoy that break, so the blog will be probably be off for a few days, I might upload some pictures, because places we’ll visit look simply amazing, but I should be back to work in a bit less than three weeks.
(updates of the trip will be on the kids blog, for those who know it).
I will be in Atlanta for the week-end, for a SoA meeting. Last time I went to an SoA meeting (in Chicago), I did mention a connexion between baseball and mathematics (and Paul Erdös). This, time, I can probably mention a connexion between basketball and acturial science. More precisely, a great basketball player named Peter “Pistol Pete” Press Maravich. In an interview in 1974 (while he was playing with the Hawks of Atlanta), Maravich had said, “I don’t want to play 10 years [in the NBA] and then die of a heart attack when I’m 40.” Unfortunately, this is what happened, somehow. On January 5th, 1988, he collapsed after a three-on-three pickup game in Pasadena, California, and died of a heart attack. Pete Maravich was 40.
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
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.
I will be in Chicago for the next few days, at the 2013 CAE Faculty Conference, organized by the Society of Actuaries,
Last week, I was involved in the PhD defense of Julien Tomas, with Rob Kaas (promotor), Frédéric Planchet (co-promotor), Katrien Antonio, Marc 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/.
The R codes will be available soon on my blog (and on Julien’s new website http://www.likelihood.me/).
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.
In a couple of days, Benoit will give a talk at the 9th Conference on Public Economics At the Regional and Local level (PEARL) in Helsinki, in Finland organized by the VATT (Government Institute for Economic Research). The slides are now available on the blog, and the paper is still online here
I am currently enjoying some holidays, I should be back soon, in Montréal (pictures will be online on the kids’blog, for those who got the address)
The blog will not be updated during holidays, so Merry Christmas to all my readers (and all those who end up here by accident). And yes, I will spend some time on the Rivera Maya,
I will be in NYC and Boston for the next three weeks…
Time for a short break… we will go South for a few days,
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.
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).
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.
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.