Short courses
The pre-conference short course (September 16-19, 2002 ) is divided into three sections:
|
Extreme values with applications in insurance and finance |
| (prof. Jan BEIRLANT & prof. Jef TEUGELS) |
Summary:
The course will be based on a forthcoming book Statistics of extremes
currently prepared by J. Beirlant, J.L. Teugels and Y. Goegebeur. The
course will contain an overview of the most important statistical problems
and solutions where the modeling of extreme values is of prime importance.
The course is built up from a statistical point of view and will contain
the statistical motivation and introduction of case studies used throughout
the course and a wealth of univariate problems and methods.
Mathematical and probabilistic proofs will typically be avoided but
references will be given at the end of the course. We will put more
emphasis on the correct application of the statistical methods resulting
from the best possible theoretical setting.
In a first section we show the importance of extreme value theory. Why is
extreme value methodology necessary and what does it add to classical
statistics? Further, domains of applications and selected case-studies are
treated. We then cover the probabilistic side of extreme value theory.
The main part of the course deals with basic univariate methods. After
dealing with the asymptotic distributions of maxima, the necessary tools
for data analysis are given: quantile-quantile plots, the extreme value QQ
plot, Pareto quantile plots and excess plots
We then pass on to tail estimation under Pareto models, treating in some
detail the Hill estimator, regression estimators and regression models for
log-spacings of extreme order statistics. Reduction of the bias will help
in the estimation of extreme quantiles and small exceedance probabilities.
The more general problem of tail estimation for maximal domains of
attraction is then covered. Procedures like the Peaks-over-Threshold method
and the method of probability weighted moments will be combined with
methods based on extreme order statistics.
All of the many examples will come from actuarial science with a major
emphasis on data from non-life insurance.
| Modelling dependence in actuarial science and finance |
| (prof. Jan DHAENE) |
Summary:
In traditional risk theory, individual risks in a portfolio are usually
assumed to be mutually independent. Assuming independence is very
convenient since the mathematics for dependent risks are less tractable,
and also because in general the statistics gathered by the insurer only
give information about the marginal distributions of the risks, not about
their joint distribution (i.e. the way these risks are interrelated). In
certain situations, however, the individual risks will not be mutually
independent because they are subject to the same claim generating mechanism
or are influenced by the same economic or physical environment. Introducing
e.g. stochastic discounting in actuarial models immediately reveals the
necessity of determining distribution functions of sums of dependent random
variables.
In case multivariate statistics are available, some interesting tools to
modelise the dependency between random variables are the copulas. The
latter are of interest to actuaries for two main reasons: first of all,
they represent a way of studying scale-free measures of dependence; and
secondly they are used as a starting point for constructing families of
bivariate distributions with a view to simulation. These aspects will be
developed during the course and several illustrations will enhance the
relevance of the copula construction in both life and non-life insurance.
In this short course, it is shown how to take into account dependency
information (if any available) and how to construct safe estimates
regarding sums of dependent random variables (if no dependency information
available).
| Building projected lifetables and managing the longevity risk |
| (prof. Michel DENUIT) |
Summary:
Mortality projections and longevity risk are major concerns for
pricing life annuities. In most industrialized countries, demographic
studies reveal decreasing annual death probabilities at old ages.
Those trends have to be incorporated in the calculation of expected
present values in order to avoid underestimation of future costs.
The course purposes to present different approaches to model trends
in mortality experience. Further, it aims to deal with the uncertainty
inherent to these projections (the so-called longevity risk). All
the methods are applied to Belgian mortality statistics.