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Talks in Actuarial Sciences
SH 11-12
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10.11.11
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Giang Nguyen
(Université Libre de Bruxelles)
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Phase-Type distributions meet Panjer's algorithm
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ULB NO 9 Salle des Professeurs, Schedule: 12-13
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Abstract: Panjer (1981) presents an efficient recursive formula for evaluating compound distributions such as compound Poisson and compound negative binomial, assuming that claim sizes are nonnegative, and identically and independently distributed, and that the claim number follows a distribution that satisfies the Panjer recursive relation. Since this seminal paper, there have been many generalizations of this standard technique in insurance, but surprisingly few generalizations involve Phase-Type distribution, a versatile distribution frequently used in approximation and simulation. We describe generalizations of the Panjer's algorithm to two cases: where both the claim number and claim sizes are Phase-Type distributed, and where only the claim number is Phase-Type distributed, and discuss the associated complexity. Furthermore, we present preliminary results on the extension of Panjer (scalar) recursive relation to a matrix recursive relation; in particular, we discuss the family of distributions that satisfy this Panjer-like matrix recursive relation.
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SE 10-11
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12.05.11
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Martino Grasselli
(Università degli Studi di Padova et ESI Leonard de Vinci)
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Riding on the Smiles
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ULB NO 5 Salle Solvay, Schedule: 16:15-17:15
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Abstract: Using a data set of vanilla options on the major indexes we investigate the
calibration properties of several multifactor stochastic volatility models by
adopting the Fast Fourier Transform as the pricing methodology. We study the
impact of the penalizing function on the calibration performance and how it
affects the calibrated parameters. We consider single asset as well as multiple-asset models, with particular
attention to the single asset Wishart Multidimensional Stochastic Volatility
model introduced in Da Fonseca et al. (2008b) and the Wishart Affine Stochastic
Correlation model proposed by Da Fonseca et al. (2007b), which provides a
natural framework for pricing basket options while keeping the stylized
smile-skew effects on single name vanillas. For all models we give some option price approximations that are very useful to speed up the pricing process. What is more, these approximations allow us to
compare different models by aggregating conveniently the parameters and they
highlight the ability of the Wishart-based models in controlling separately the
smile and the skew effects. This is extremely important in a risk management
perspective of a book of derivatives that includes exotic as well as basket
options.
This is Joint work with Jose da Fonseca (Auckland University of Technology).
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15.03.11
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Carole Bernard (University of Waterloo, Canada)
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Financial Bounds for Insurance Prices
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ULB NO 5 Salle Solvay, Schedule: 17:00-18:00
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Abstract: Equity-linked insurance contracts contain financial risk and mortality
risk: they cannot be fully hedged in the financial market. In the presence of a complete financial market, we show how to calculate market-consistent insurance prices using an indifference principle. In this context and with very mild assumptions on agents' preferences, we derive upper and lower bounds for insurance claims' prices. These bounds correspond to the market prices of some explicitly known financial payoffs. These bounds are also robust in the sense that they are likely to be agreed on by all market participants.
This is Joint work with Prof. Steven Vanduffel (Vrije Universiteit Brussel).
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27.01.11
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Fraser Daly (University of Bristol, UK)
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Smoothing estimates in total variation distance using Stein's method
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ULB NO 5 Salle Solvay, Schedule: 11:00-12:00
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Abstract: Consider the approximation of a discrete random variable. It is often desirable to achieve a closer approximation and better rate of convergence than is possible using a simple one-parameter Poisson approximation. One alternative is to approximate by a two-parameter distribution, such as a translated (or centered) Poisson distribution. One major obstacle to useful applications of some approximation theorems in this setting is the need for smoothing bounds in total variation distance: bounds on the total variation distance between some random variable and a translated version of the same random variable. Such bounds are available in only a limited number of cases. In this talk we will see two related approaches to finding such smoothing bounds in more general settings, based on Stein's method for probability approximation.
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SH 10-11
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21.10.10
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Maude Gathy (Université Libre de Bruxelles)
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On Katz/Panjer type recursions with applications to insurance
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ULB NO 906, Schedule: 17:15-18:15
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Abstract: In insurance, the main usefulness of the classical Katz/Panjer recursion is to yield a simple recursive algorithm for the aggregate claims distribution (Panjer (1981)).
The present talk is first concerned with the Markov-Pólya distribution and its links with the Katz/Panjer family of distributions. The Markov-Pólya distribution is presented as a claim frequency model incorporating some (anti)contagion effects. This distribution is shown to satisfy a Katz/Panjer-like recurrence and this enables us to derive a simple Panjer-like algorithm. The presentation is then focused on the Lagrangian Katz family of distributions which also satisfies an extended recursion depending this time on three parameters. The index of dispersion, an extended Panjer algorithm and the asymptotic tail behaviour of the family are then presented. Finally, the relevance of the family is illustrated with several data sets on the frequency of car accidents.
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18.11.10
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Ronnie Loeffen (Weierstrass Institute, Berlin, Germany)
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The Ornstein-Uhlenbeck type risk model: absolute ruin and spectral representation
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ULB NO 906, 16:30-17:30
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Abstract: We consider an insurance risk process modeled by a mean-fleeing Ornstein-Uhlenbeck type process with a subordinator as the background driving process. In this model the company earns interest on positive surplus and pays interest (at the same rate) when the surplus is negative. It is possible that the company gets absolutely ruined, which is the event where the premium income can no longer compensate for the interest payments. In this talk we provide simple expressions for the Laplace transform in space of both the finite- and infinite-time absolute ruin probability. Crucial in the derivation is the fact that our risk process is in some sense dual to another Ornstein-Uhlenbeck type process, namely the one that was introduced by Barndorff-Nielsen and Shephard in
finance to model stochastic volatility. For the latter process, we give under some conditions a spectral representation for its transition density, which is the analogue of the well-known spectral representation for the classical Ornstein-Uhlenbeck process. As a first application, this representation allows us to quickly compute finite-time absolute ruin probabilities.
This is joint work with P. Patie (Université Libre de Bruxelles)
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02.12.10
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Florin Avram (Université de Pau et des Pays de l'Adour, France)
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On symbolic solutions for quasi-birth-and-death processes
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ULB NO 5, Salle Solvay, 16:30-17:30
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Abstract: We consider two study cases for evaluating the utility of "algebraic analysis" methods:
retrial queues, for which explicit solutions exist only when the number of servers
is less than two Kawanishi's model, a level independent quasi-birth-death process
with explicit transition probabilities (obtainable by Lie's approach of computing exponentials
of operators).
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09.12.10
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Vincent Vigon (Université Louis Pasteur, Strasbourg, France)
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TBA
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ULB NO 5, Salle Solvay,
16:30-17:30
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Abstract: :
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SE 09-10
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18.02.09
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Paul Lescot (Université de Rouen, France)
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Isovecteurs pour l' équation de Black-Scholes
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ULB NO 906, 16:30-17:30
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Abstract: Le calcul du groupe des symétries d'une équation aux dérivées partielles au moyen de la méthode des isovecteurs s'est révélé très utile en physique mathématique classique (cf.Harrison-Estabrook, Journal of Mathematical Physics, 1971), ainsi qu'en mécanique quantique euclidienne (cf. Lescot-Zambrini, Progress in Probability, vols 58 and 59).
Nous déterminons les isovecteurs pour l' équation de Black-Scholes en utilisant une méthode similaire à celle employée dans le cas de l' équation de Hamilton-Jacobi-Bellman dans nos deux articles suscités. Ce calcul permet de rendre conceptuellement limpide la
solution originale par Black and Scholes (Journal of Political Economy, 81(3),1973) de leur équation. Comme corollaire, nous obtenons d'intéressantes transformations sur l'espace des solutions.
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23.04.10
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Journée de Contact FNRS, Groupe Sciences Actuarielles, Université Libre de Bruxelles
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Programme complet (.pdf)
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9h15-9h45: Marie Chazal (Université Libre de Bruxelles)
Option pricing in affine term structure models
9h45–10h30: David Vyncke (Ghent University)
Measuring dependence for aggregating risks
11h00–11h45: Freddy Delbaen (ETH Zurich)
BSDE with pathwise square bounded driver
11h45–12h15: Grégory Rayée (Université Libre de Bruxelles)
Volatility pricing models for long-dated foreign exchange derivatives
14h15–15h00: Andreas Kyprianou (Bath University)
Meromorphic Lévy processes
15h00–15h45: Laura Ballotta (Cass Business School, City University London)
Investment strategies and risk management for participating life insurance contracts
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SH 09-10
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22.10.09
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Julien Trufin (Université Catholique de Louvain, Belgium)
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Credibility theory and ultimate ruin probability
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ULB NO 906, 16:30-17:30
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Abstract: In this talk, we consider a ruin model where experience rating will be taken into account. Allowing the premium amount to depend on past claims experience through an appropriate credibility mechanism is in line with insurance practice in most business lines. In this setting, the main purpose is to investigate the behavior of the
ultimate ruin probabilities for large initial capital in the case of light-tailed claim amounts. First, the logarithmic asymptotics behaviour of the ultimate ruin probability will be derived. Then, typical pathes leading to ruin will be studied. Also, an upper bound will be derived on the ultimate ruin probability in some particular case.
Finally, the influence of the number of data taking into account will be studied. A word about heavy-tailed claims will be done.
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19.11.09
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Ronnie Loeffen (Weierstrass Institute, Berlin, Germany)
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De Finetti's optimal dividends problem with an affine penalty function at ruin
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ULB NO 906, Schedule: 17:30-18:30
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Abstract: De Finetti's optimal dividends problem is the quest for the dividend policy maximizing the expected present value of the dividend payments made by an insurance company. In a Lévy insurance risk model, we will look at a generalization of the problem in which the company is penalized for (early) ruin. We will show that when the tail of the Lévy measure is log-convex, then, except in some rare cases, the optimal strategy takes the form of a barrier strategy. The key step in the proof is the result that, under the aforementioned condition on the jump measure, the scale function of the spectrally negative Lévy process has a log-convex derivative. The latter follows from a certain monotonicity property of renewal functions.
This is joint work with J.-F. Renaud (University of Waterloo)
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26.11.09
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Tetyana Kadankova (Vrije Universiteit Brussel, Belgium)
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Ruin theory and the two-sided exit problems for several classes of stochastic
processes
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ULB NO 906, 16:30-17:30
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Abstract: In this talk, we deal with the so called boundary problems (one- and two-sided exit problems and
others) of Lévy processes and some related processes. These are problems of determining the law of the first passage of a level (first exit time
from a fixed interval) by the process and other characteristics such as position of the process at
this instant, the value of the overshoot through the level, the sojourn time inside the interval,
the number of intersections of the interval, etc. The importance of this study stems from the
fact that the first passage problems and the first exit problems are directly connected with
determining the distribution of buffer overflow, bankruptcy of a firm, the price of a two-barrier
option, etc.
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Last update: Oct. 2010 by Pierre Patie