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\begin{center}
{\huge\bf Risk Day 2003\\}
\bigskip
{\large Mini-Conference on\\
Risk Management in Finance and Insurance}\\
\medskip
Friday, October 17, 2003\\
ETH Z\"urich, Main Building, Lecture Theatre HG F5\\
\bigskip\medskip
{\large \bf Program}
\end{center}
\vspace{-2mm}
\begin{tabular}{@{}lp{124mm}}
9.00 -- 9.10 &  Prof.~Dr.~Paul Embrechts 
                (Department of Mathematics, ETH Z\"urich)\newline 
                {\it Welcome and Introduction}\\[\smallskipamount]
9.10 -- 9.20 &  Eckart J\"ager
                (NCCR FINRISK, Swiss Banking Institute, Univ.~of Z\"urich)\newline 
                {\it Presentation of the Doctoral Program in Finance
                at the Univ.~of Z\"urich}\\[\smallskipamount]
9.20 -- 10.00 & Prof.~Dr.~Martin Schweizer
                (Department of Mathematics, ETH Z\"urich)\newline 
                {\it Pricing and Hedging Recursive Payoff Structures}\\[\smallskipamount]
10.00 -- 10.30& Dr.~Hansj\"org Furrer (RiskLab, ETH Z\"urich)\newline
                {\it Quantifying Regulatory Capital for Operational Risk}\\[\smallskipamount]
10.30 -- 11.00& Coffee Break (Main Hall, F-Floor, Uhrenhalle)\\[\smallskipamount]
11.00 -- 11.40& PD Dr.~Wolfgang Breymann (RiskLab, ETH Z\"urich)\newline
                {\it An Intraday Analysis of Diversified World Stock Indices}\\[\smallskipamount]
11.40 -- 12.10& Jonathan Wendin (Department of Mathematics, ETH Z\"urich)\newline
                {\it Generalized Linear Mixed Models in Portfolio
                Credit Risk Modelling}\\[\smallskipamount] 
12.10 -- 13.50& Lunch Break\\[\smallskipamount]
13.50 -- 14.30& Dr.~Juri Hinz (University of T\"ubingen)\newline
                {\it On Valuation of Electricity Contracts}\\[\smallskipamount]
14.30 -- 15.00& Michael Kupper (Department of Mathematics, ETH Z\"urich)\newline 
                {\it Coherent and Convex Risk Measure for c\`adl\`ag Processes}\\[\smallskipamount]
15.00 -- 15.30& Prof.~Dr.~Philipp Sch\"onbucher
                (Department of Mathematics, ETH Z\"urich)\newline
                {\it Frailty Models, Contagion and Information Effects}\\[\smallskipamount]
15.30 -- 16.00& Coffee Break (Main Hall, F-Floor, Uhrenhalle)\\[\smallskipamount]
16.00 -- 16.30& Dr.~Daniel Straumann (RiskLab, ETH Z\"urich)\newline
                {\it Maximum Likelihood and Quasi Maximum Likelihood Estimation}\newline
                {\it in Conditionally Heteroscedastic Time Series Models}\\[\smallskipamount]
16.30 -- 17.00& Filip Lindskog (RiskLab, ETH Z\"urich)\newline
                {\it On Regular Variation for Stochastic Processes}
\end{tabular}

\bigskip%\smallskip
\centerline{\large \bf General Information}
\medskip
Participation is free and there is no official registration. Everyone is
welcome, practitioners are especially encouraged to attend. There are no
special arrangements for lunch since there are sufficient possibilities
nearby, in particular at ETH and the University.
%There is also the Dozentenfoyer.
\par
\medskip
{\sc Local Organisers:}\par
Prof.~Dr.~Uwe Schmock (Financial and Actuarial Math., Vienna University of Technology)\par
Prof.~Dr.~Philipp Sch\"onbucher (Department of Mathematics, ETH Z\"urich)\par
{\sc Conference Secretary}: Mrs Irma Drack, CLP D4 (IFOR),
Phone $+$41-1-632 40 16\hfil\break E-mail: drack@ifor.math.ethz.ch\par
{\sc Risk Day 2003 Web Page:} 
http://www.math.ethz.ch/finance/Risk-Day-2003.html
\pagebreak


\centerline{\bf\Large Risk Day 2003}
\medskip
\centerline{\bf\Large Abstracts}
\bigskip\medskip

Prof.~Dr.~Martin Schweizer,
{\bf Pricing and Hedging Recursive Payoff Structures}
\smallskip

{\sc Abstract:} We discuss some ideas in the context of pricing and hedging
financial structures whose payoffs are defined in terms of their valuation---for
instance defaultable bonds or certain insurance products. This leads to a recursive
definition of the value process associated to such a structure, and we present a
class of stochastic models where such products can be handled by using PDE methods.
This is joint work with Dirk Becherer. Discretizing these models also leads to
interesting new convergence problems, and we touch upon this issue as well.
\looseness=-1
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}mschweiz/}

Email:
{\tt mschweiz@math.ethz.ch}
\bigskip\smallskip

Dr.~Hansj\"org Furrer,
{\bf Quantifying Regulatory Capital for Operational Risk}\smallskip

{\sc Abstract:} The proposed New Basel Capital Accord (Basel~II) established by the
Basel Committee on Banking Supervision calls for an explicit treatment of
operational risk. Banks are required to demonstrate their ability to capture severe
tail loss events. Value-at-risk is a risk measure that could be used to derive the
necessary regulatory capital. Yet operational loss data typically exhibit
irregularities which complicate the mathematical modeling. It is shown that
traditional modeling approaches, including extreme value theory, reach their limits
as the structure of operational loss data is barely in line with the modeling
assumptions.\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}hjfurrer/}

Email:
{\tt hjfurrer@math.ethz.ch}
\bigskip\smallskip

PD Dr.\kern-0.1em~Wolfgang Breymann,
{\bf An Intraday\kern-0.1em\ Analysis of Diversified World Stock Indices}\smallskip

{\sc Abstract:} 
This talk proposes an approach to the intraday analysis of diversified world
accumulation indices. The growth optimal portfolio (GOP) is used as reference unit
or benchmark in a continuous financial market model. Diversified global portfolios,
covering the world financial market, are constructed and shown to approximate the
GOP\kern0pt. The normalized GOP is modeled as a time transformed square root process of
dimension four. Its dynamics is empirically verified in a robust manner for several
world stock indices. Furthermore, the long-term evolution of the transformed time is
modeled via a constant net growth rate of the drift of the discounted GOP and a
quickly evolving market activity. The latter is decomposed into a mean reverting
stochastic market activity process and a deterministic seasonal market activity
component. The empirical findings identify a simple and realistic model for a world
stock index that reflects its historical evolution reasonably well by using only a
few constant parameters. (This is joint work with Leah Kelly and Eckhard Platen.)
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}breymann/}

Email:
{\tt breymann@math.ethz.ch}

\bigskip\smallskip

Jonathan Wendin,
{\bf Generalized Linear Mixed Models in Portfolio Credit Risk Modelling}
\smallskip

{\sc Abstract:} A crucial point in portfolio credit risk modelling is that of
dependence among default events. One way of handling this is given by Generalized
Linear Mixed Models (GLMMs); a well-known concept in statistics for dealing with
repeated measurements on different units. This talk gives a general introduction to
GLMMs with problems relating to portfolio credit risk in mind. In this setting
default probabilities or default intensities are viewed as a result of both fixed
effects and random effects, where the latter are the key to dependence between
counter-party defaults. By choosing the random effects suitably we obtain dependence
between defaults in a given year as well as dependence between defaults in
consecutive years---two kinds of dependence that have been observed in empirical
default data. 
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}wendin/}

Email:
{\tt wendin@math.ethz.ch}
\bigskip\smallskip


Dr.~Juri Hinz,
{\bf On Valuation of Electricity Contracts}
\smallskip

{\sc Abstract:}
Beginning in the nineties a number of electricity markets have been deregulated. The
enforced competition in electricity production, retail, and trading raises various
problems concerning optimal market design, price risk management, and strategy
optimization. In this talk, we outline a special topic in this area elaborating on
real assets. The idea here is that, since electricity is not storable, the true
underlying will be the ability to produce power. Calculating equilibrium prices for
production capacites, we obtain a valuation of contracts which is fair in the sense
that arbitrage is excluded for capacity and claim trading. 
\smallskip

Home page:
{\tt http://zufall1.mathematik.uni-tuebingen.de/hinz.html}

Email:
{\tt juri.hinz@uni-tuebingen.de}
\bigskip\smallskip


Michael Kupper,
{\bf Coherent and Convex Risk Measure for c\`adl\`ag Processes}
\smallskip

{\sc Abstract:} If the random future evolution of values (such as the market value of
a firm's equity, the market value of a portfolio of financial securities or the
surplus of an insurance company) is modelled in continuous time, then a risk measure
can be seen as a functional on the space of stochastic processes. We extend the
notions of coherent and convex risk measures to the space of bounded c\`adl\`ag
adapted processes. We present representation results based on convex duality theory
and show that under a weak continuity assumption (Fatou property) the representation
holds in terms of $\sigma$-additive optional random measures. Furthermore, we discuss an
extension to the space of unbounded processes. As an example, we calculate the risk
of a classical Cram\'er--Lundberg process under a given coherent risk measure and
compare it with classical results. (This is joint work with Patrick Cheridito and
Freddy Delbaen.)\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}kupper/}

Email:
{\tt kupper@math.ethz.ch}
\bigskip\smallskip


Prof.~Dr.~Philipp Sch\"onbucher
{\bf Frailty Models, Contagion and Information Effects}
\smallskip

{\sc Abstract:} Most of the existing literature on default contagion
assumes a direct causal relationships between two obligors'
defaults. In contrast to this we show in this talk that
default contagion can also arise from information
effects if investors are imperfectly informed about
some common factors affecting the true riskiness of
the obligors. We model this effect in a simple
extension of the intensity-based modelling framework using
unobserved frailty variables. The default intensities in this
model exhibit jumps at default events of other obligors.
This entails much higher (and more realistic) levels of
default dependence between the obligors than what purely
diffusion-based intensity models were able to capture
previously, without adding too much additional complexity.
The parameters of the dependence can be implied directly
from spread jumps observed in the market, thus enabling
a full specification of the model under pricing probabilities
without recourse to historical default correlations. We
furthermore present two extensions of the model: The first
extension shows that the size of the contagion effect can
depend on the reason for the default and not just the identity
of the defaulted obligor, the second extension exhibits
stochastic default correlation.
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}schonbuc/}

Email:
{\tt p@schonbucher.de}
\bigskip\smallskip


Dr.~Daniel Straumann,
{\bf Maximum Likelihood and Quasi Maximum Likelihood
Estimation in  Conditionally Heteroscedastic Time Series Models}
\smallskip

{\sc Abstract:}
By exploiting the techniques of stochastic recurrence equations, we 
develop a general and unifying limit theory for the maximum likelihood  estimator
(MLE) and quasi maximum likelihood estimator (QMLE) in a  certain parametric class of
conditionally heteroscedastic processes, which contains widely used financial time
series models:  (asymmetric) GARCH(1,1) and EGARCH. Our approach  generalizes and
clarifies work of Lumsdaine (1996) and Berkes et al.\ (2003). We furthermore discuss
the issue of misspecification  in the MLE and the behavior of the QMLE in the
presence of a heavy-tailed noise distribution. This complements work  by Newey and
Steigerwald (1997) and Hall and Yao (2003). (The talk is based on my Ph.D.\ thesis.)
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}strauman/}

Email:
{\tt strauman@math.ethz.ch}
\bigskip\smallskip


Filip Lindskog,
{\bf On Regular Variation for Stochastic Processes}
\smallskip

{\sc Abstract:}
We study a formulation of regular variation on the space of ${\Bbb R}^d$-valued
right-continuous functions on $[\mskip1.5mu0,1]$ with left limits and provide necessary and
sufficient conditions for a stochastic process with sample paths in this space to be
regularly varying. A version of the Continuous Mapping Theorem is proved which
enables the derivation of the tail behavior of rather general mappings of the
regularly varying stochastic process. For a wide class of Markov processes with
asymptotically independent increments we obtain simplified sufficient conditions for
regular variation. For such processes we show that the possible regular variation
limit measures concentrate on step functions with one step, from which we conclude
that extremes for such processes are due to one big jump in $(0,1]$ or an extreme
starting point. Finally, using the Continuous Mapping Theorem we derive the tail 
behavior of filtered regularly varying Markov processes with  asymptotically
independent increments. (This is joint work with Henrik Hult.)
\smallskip

Home page:
{\tt http://www.math.ethz.ch/\lower3pt\hbox{\~{}}lindskog/}

Email:
{\tt lindskog@math.ethz.ch}

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