Parution d’un court article sur la Théorie de la Crédibilité dans la revue Risques.
La théorie de la crédibilité est une jolie application de l’approche bayésienne de la statistique, puisque l’on cherche à déterminer la probabilité d’appartenir à une classe de risque conditionnellement à une expérience de sinistralité observée. La théorie développée par Hans Bühlmann propose d’ailleurs de jolies applications, en particulier sur les jeux de fléchettes, où l’on compare la moyenne sur un sous-groupe homogène (ou supposé l’être) avec la moyenne de la population totale. En faisant intervenir des variance intra et des variances inter, on arrive à un résultat relativement simple et élégant.
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.
Parution de l’article Estimating allocations for Value-at-Risk portfolio optimization dans Mathematical Methods of Operations Research.
Value-at-Risk, despite being adopted as the standard risk measure in finance, suffers severe objections from a practical point of view, due to a lack of convexity, and since it does not reward diversification (which is an essential feature in portfolio optimization). Furthermore, it is also known as having poor behavior in risk estimation (which has been justified to impose the use of parametric models, but which induces then model errors). The aim of this paper is to chose in favor or against the use of VaR but to add some more information to this discussion, especially from the estimation point of view. Here we propose a simple method not only to estimate the optimal allocation based on a Value-at-Risk minimization constraint, but also to derive— empirical—confidence intervals based on the fact that the underlying distribution is unknown, and can be estimated based on past observations.
Je met en ligne un (court) papier sur l’augmentation du nombre de naissance les jours de pleine lune, Lunar cycles and birth rates: from a full Moon to a first quarter Moon effect
Objective The purpose of this study was to examine the influence of the lunar cycle on the frequency of deliveries.
Method This was a time series of 29,385,552 births across 470 lunar cycles that were identified from the French National Institute of Statistics from 1968 to 2005.
Results Using nonparametric smoothing techniques to remove patterns, t-tests validated a significant difference in the number of births on a short window around the full Moon, stress by a significant drop after the first quarter Moon.
Conclusion An analysis of 37 years of data demonstrated a small but statistically significant influence of the lunar cycle on deliveries.
The paper on Convergence of Archimedean Copulas, with Johan Segers, just appeared, in Statistics and Probability Letters.
Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed.
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.
Modeling the 2003 heatwave in Paris (paper)
In February 2005, opening the conference on Climate change: a global, national
and regional challenge, chairman Dennis Tirpak pointed out that there is no
longer any doubt that the Earth’s climate is changing […] globally, nine of
the past 10 years have been the warmest since records began in 1861“. He
singled out the heatwave that gripped western Europe in 2003 as an example:
Europe’s worst natural disaster in 50 years killed as many as 40; 000 people
and inflicted an estimated 30 billion dollars in damage. Hence, the summer of
2003 will be remembered for the extreme heat, and the approximately 40,000
heat-related deaths over western Europe (from 30,000 up to more than 52,000
depending on the source). More specifically, the period 1-15 August 2003 was
the most intense heat of the summer. The report of Pirard et al. (2005) states
that Europe experienced an unprecedented heat wave in the Summer 2003. In
France, it was the warmest summer recorded for 53 years in terms of minimal,
maximal and average temperature and in terms of duration” […]
Conférence Insurance and Adaptation to Climate Change, Paris, Mars 2007. The paper appeared in the Geneva Papers.
The IPCC 2007 report noted that both the frequency and strength of hurricanes, floods and droughts have increased during the past few years. Thus, climate risk, and more specifically natural catastrophes, are now hardly insurable: losses can be huge (and the actuarial pure premium might even be infinite), diversification through the central limit theorem is not possible because of geographical correlation (a lot of additional capital is required), there might exist no insurance market since the price asked by insurance companies can be much higher than the price householders are willing to pay (short-term horizon of policyholders), and, due to climate change, there is more uncertainty (and thus additional risk). The first idea we will discuss in this paper, about insurance markets and climate risks, is that insurance exists only if risk can be transferred, not only to reinsurance companies but also to capital markets (through securitization or catastrophes options). The second one is that climate is changing, and therefore, not only prices and capital required should be important, but also uncertainty can be very large. It is extremely difficult to insure in a changing environment.
The paper was presented in a conference, in Paris, in 2007
The paper (with David Sibai) on High Frequency models in hydrology just appeared, in Environmetrics.
When working on river floods—annual river levels maxima—, two approaches are usually considered: one inspired from Emil Gumbel where annual maxima are supposed to be i.i.d. and distributed according to Gumbel’s distribution, and one inspired from Edwin Hurst where annual maxima are strongly dependent, and exhibit long range memory. This paper tries to solve this apparent paradox by deriving a dynamic model inspired from financial models, which does not take into account annual maxima only but also threshold exceedances. It studies the implications of such a paradox in terms of return period—a notion valid as long as the data are i.i.d—and of extremal events.