- List of participants - | |
- Group photo - |
SCHEDULE |
MONDAY 26TH | TUESDAY 27TH | WEDNESDAY 28TH | THURSDAY 29TH | FRIDAY 30TH | ||||||||||
9h30 - 9h45 | Welcome | 9h00 - 10h00 | Course
1.2![]() |
9h00 - 10h00 | Course
2.2![]() |
9h00 - 10h00 | Course
1.3![]() |
9h00 - 10h00 | Course 1.4![]() |
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9h45-10h45 | Course
1.1![]() |
10h15-11h15 | Course
2.1![]() |
10h15-11h00 | Balan | 10h15-11h15 | Course
2.3![]() |
10h15-11h15 | Drees![]() |
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11h15-12h15 | 11h30-12h30 | Loisel![]() |
11h15-12h00 | Nolan | 11h30-12h30 | Samorodnitsky![]() |
11h30-12h30 | Beirlant![]() |
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Lunch | Lunch | 12h00-12h30 | Stoev | Lunch | Lunch | |||||||||
15h30-16h15 | Leipus![]() |
16h00-16h45 | Maume-Deschamps![]() |
Lunch | 16h00-16h45 | Kulik![]() |
13h45-14h30 | Puccetti![]() |
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16h15-16h45 | Siaulys![]() |
16h45-17h15 | Bäuerle![]() |
Free Afternoon LINK | 16h45-17h15 | Di
Bernardino![]() |
14h30-15h00 | Robert![]() |
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16h45-17h30 | Collamore![]() |
17h30-18h00 | Constantinescu![]() |
17h30-18h30 | Davis |
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18h00-18h30 | Mikosch![]() |
18h00-18h30 | Cossette![]() |
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18h30-19h15 | Tang![]() |
18h30-19h15 | Marceau![]() |
COURSE 1 |
Henrik Hult: Four lectures on importance sampling
To Schedule |
COURSE 2 |
Sophie Hautphenne: Matrix analytic methods Erlangization
To Schedule |
MONDAY 26TH APRIL |
15h30-16h15 Remigijus Leipus
Asymptotics of random
sums of heavy-tailed negatively dependent random variables with
applications
Let
be negatively dependent and identically distributed random variables
having dominatedly varying tails, and let
be a counting random variable independent of
's.
In this paper, we obtain the asymptotics for the tail probability of
the random sum
, where the tail
of
is comparable with, heavier or
lighter than that of
.
16h15-16h45 Jonas Siaulys
Local precise large
deviation results for sums of random variables with O-regularly varying
densities
We establish local precise large deviation results for sums
of independent
and identically distributed random variables
with
-regularly
varying density
and distribution function
.
The asymptotic behavior of the probability
is
comparable, for fixed
,
with quantities
or
.
16h45-17h30 Jeffrey Collamore
On Cramér-Lundberg
theory with stochastic investments and its dual financial process
This talk will be concerned with risk estimates relating to a class of
random recurrence equations. Our original motivation came from the ruin
problem with investments, where an insurance company invests its excess
capital and earns stochastic interest on these investments. A similar
problem arises when studying the stationary tail behavior of the
GARCH(1,1) financial process. Both processes exhibit temporal
dependence, which cannot be analyzed by classical techniques.
The tail behavior for these processes is usually obtained by
observing that they satisfy a random recurrence equation, namely,
where
is a random
function and
is a random variable on
.
A
well-known result of Goldie (1991) then states that
![]() ![]() |
(1) |
In this talk, we will introduce an alternative approach to Goldie's. In particular, we will begin by describing a duality connecting Cramér-Lundberg models with stochastic investments to an extended GARCH(1,1) financial process. Using this duality, we then establish the sharp upper bound
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To Schedule |
TUESDAY 27TH APRIL |
16h00-16h45 Véronique
Maume-Deschamps Multivariate risk
indicators: estimation and application to optimal reserve allocation.
We consider some risk indicators of vectorial risk processes. These
indicators are expected sums of some penalties that each line of
business would have to pay due to its temporary potential insolvency.
The dependency between lines of business is taken into account. By
using stochastic algorithms, we may estimate the minimum of these risks
indicators, under a fixed total capital constraint. This minimization
may apply to optimal reserve allocation.
(Joint work with
Peggy Cenac and Clémentine
Prieur.)
16h45-17h15 Nicole Bäuerle
Multivariate Risk
Processes with Interacting Intensities
The classical models in risk theory consider a single type of claims.
In the insurance business, however, several business lines with
separate claim arrival processes appear naturally, and the individual
claim processes may not be independent. We introduce a new class of
models for such situations, where the underlying counting process is a
multivariate continuous time Markov chain of pure birth type and the
dependency of the components arises from the fact that the birth rate
for a specific claim type may depend on the number of claims in the
other component processes. Under certain conditions we obtain a fluid
limit, i.e. a functional law of large numbers for these
processes. We also investigate the consequences of such results for
questions of interest in insurance applications. Several specific
subclasses of the general model are discussed in detail and the Cramér
asymptotics of the ruin probabilities are derived in particular cases.
(This is a joined
work with Rudolf Grübel.)
17h30-18h00
Corina Constantinescu
Symbolic Computation for
Boundary Problems in Risk Theory
In this talk we will present a symbolic computation approach
to
boundary problems, based on operators, that is applicable in risk
theory.
The main idea is to reduce the integral equations satisfied
by functions of the risk processes to boundary problems. Further, one
can factorize these problems into first order boundary problems, which
will often allow to derive explicit expressions for the functions
considered. For instance, one can find explicit expressions for
the Gerber-Shiu functions in terms of the penalty function,
in
quite general settings.
18h00-18h30 Helene Cossette
Discrete-time risk models
based on time series for count random variables
In this talk, we consider risk models based on time series models for
count random variables, which can be applied in the context of
accidents. Examples of time series models for count data are integer
value moving average models and integer value autoregressive models. We
examine the properties of the total amount of (discounted or not)
claims over a fixed number of periods. We analyze the dangerousness of
the risk models through the measurement of the adjustment coefficient.
Ruin measures are also examined.
18h30-19h15
Etienne
Marceau
Agrégation des risques
dépendants et allocation du capital
Dans cet exposé, nous considérerons un portefeuille constitué de
risques dépendants (contrats d'assurance, lignes d'affaires, etc.). La
relation de dépendance entre les risques est fondée sur des copules,
des modèles multivariés composés ou des modèles avec mélange commun.
Nous examinons diverses méthodes d'agrégation des risques dépendants
adaptées aux modèles de dépendance considérés. Ces méthodes nous
permettent d'aborder l'évaluation des mesures de risque Value-at-Risk
(VaR) et Tail-Value-at-Risk (TVaR) et l'allocation du capital aux
composantes du portefeuille de risque. Dans le cas des modèles de
dépendance fondés sur les mélanges communs, nous examinons aussi la
part de capital associé au risque systématique associé aux facteurs
aléatoires communs induisant la dépendance entre les risques. Des
exemples numériques sont présentés dans le but d'illustrer les notions
présentés.
To Schedule |
WEDNESDAY 28TH APRIL |
10h15-11h00 Raluca Balan A
cluster limit theorem for
infinitely divisible point processes
In
this talk, we examine the connection between the limit representation
of an infinitely divisible point process, and its cluster
representation. Our result identifies some explicit conditions for the
convergence of the sequence of point processes associated to a
triangular array of random variables, in terms of the probabilistic
behavior of the variables in the array. As applications, we discuss the
exceedance processes and the extremal index.
(Joint work with
Sana Louhichi.)
11h15-12h00 John Nolan
Classes of multivariate
max stable distributions and their relationships
We examine classes of multivariate max stable distributions and look at
their relationships to each other. One group of
models is found by directly starting with a known
angular measure. Here the class of discrete angular measures
is particularly tractable in any dimension. We then
explore a class of tractable (at least in two dimension) models with
piecewise polynomial density for the angular measure.
Another group of models is the family of common models is the family of
generalized asymmetric logistic models. We detail the
connection between this class of models and the closely related class
of generalized stable mixture class.
(Joint work with
Anne-Laure Fougères and Cécile Mercadier)
12h00-12h30 Stilian Stoev
Tail behavior of
Holder norms
and limit theorems for maxima in Holder spaces
We discuss some work in progress on functional limit theorems of maxima
in
Holder spaces. It turns out that the classical tightness conditions of
Lamperti readily apply, provided that one can control the tail-behavior
of
Holder norms of certain random processes. A powerful isomorphism
theorem of
Ciesielski allows one to obtain useful bounds on the tails of these
Holder
norms. Some implications on the path regularity of max-stable processes
will be discussed.
To Schedule |
THURSDAY 29TH APRIL |
11h30-12h30 Gennady Samorodnitsky
Long Strange
Segments, Ruin Probabilities and the Effect of Memory on Moving Average
Processes
We obtain the rate of growth of multivariate long strange segments and
the rate of decay of infinite horizon multivariate ruin probabilities
for a class of infinite moving average processes with exponentially
light tails. The rates are computed explicitly. We show that the rates
are very similar to those of an i.i.d. process as long as moving
average coefficients decay fast enough. If they do not, then the rates
are significantly different. This demonstrates the change in the length
of memory in a moving average process associated with certain changes
in the rate of decay of the coefficients.
(Jointly with
Souvik Ghosh.)
16h00-16h45
Rafal Kulik
Tail empirical process
for some long memory sequences
We
describes limiting behaviour of tail empirical process associated with
some long memory models. We show that such process has dichotomous
behaviour, according to an interplay between a Hurst parameter and a
tail index. In particular, the limit may be non-Gaussian and/or
degenerate, indicating an influence of long memory. On the other hand,
tail empirical process with random levels never suffers from long
memory. This is very desirable from a practical point of view, since
such the process may be used to construct Hill estimator of the tail
index. To prove our results we need to establish several new results
for regularly varying distribution functions, which may be of
independent interest.
(This is a joint
work with Philippe Soulier.)
16h45-17h15
Elena Di Bernardino
Estimating Bivariate
Tails
In this work we consider the general problem of estimating the tail of
a bivariate distribution. An extension of the threshold method for
extreme values is developed, using a two-dimensional version of the
Pickands-Balkema-de Hann Theorem. We construct a two-dimensional tail
estimator and we provide its asymptotic properties. The dependence
structure between the marginals is described by a copula. Simulations
are implemented.
17h30-18h30 Richard Davis
Measuring
Extremal Dependence for Time Series and Spatial Processes
via the Extremogram
The extremogram was developed as
a tool for assessing various types of extremal dependence in a
multivariate time series. The use of the extremogram in
applications arising in both financial and environmental contexts will
be illustrated. Currently, bootstrapping methods are being
adapted to the extremogram in order to construct more meaningful and
useful inference procedures. These techniques, as well as permutation
procedures, will be demonstrated in several
examples.
(This is joint
work with Thomas Mikosch and Ivor Cribben.)
To Schedule |
FRIDAY 30TH APRIL |
10h15-11h15
Holger Drees
Bootstrapping Blocks
Estimators of the Extremal Index: How Empirical Cluster Processes
Make Your Life Easy.
Recently
Drees and Rootzén (2010) have introduced a very general class of
empirical processes (indexed by functions) which describe certain
aspects of the extreme value behavior of time series. Moreover they
have proved the asymptotic normality of these processes under suitable
mixing conditions.
We apply this theory to examine the asymptotic
properties of smoothed blocks estimator of the extremal index. In
addition, we discuss how the distribution of their estimation error can
be approximated using a bootstrap approach. To this end, the limiting
behavior of multiplier block bootstrap versions of the empirical
processes conditional on the original data turns out to be vitally
important.
Drees, H., and
Rootzén, H. (2010).
Limit Theorems for Empirical Processes of Cluster Functionals, to appear in the Annals
of Statistics.
11h30-12h30 Jan Beirlant
Bias reduction in extreme
value methods: a personal perspective
The last decade
several bias-correction methods have appeared in the estimation of the
extreme value index (positive or real-valued), extreme quantiles or
large return periods. One important motivation is to construct
estimation methods where the results are less dependent on the choice
of the threshold or the number of extremes used in the estimation. We
review different methods and discuss different points of
interest in this matter:
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Free afternoon on wednesday |
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List of participants |
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Group photo |
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