IV EDITION OF THE CONFERENCE
INVITO
ALLA FINANZA MATEMATICA
and
LECTURES ON
MATHEMATICAL FINANCE
|
|
ROME,
JUNE 4, 2004 Dipartimento
di Matematica Università
di Roma “Tor Vergata”
|
|
Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×Ø×
The conference will take place on June 4,
2004, at the Department of Mathematics of the Università di Roma-Tor Vergata, supported
by the MURST PRIN project “Processi Stocastici, Calcolo Stocastico e
Applicazioni” and by the Department of Mathematics.
The conference is
divided in two parts:
· Invito alla Finanza Matematica, especially
addressed to students (e.g. laurea, master, PhD ones-in italian)
· Lectures on Mathematical Finance,
for researchers already interested in finance problems
and will include invited talks on
·
finance economics
·
risk modeling
·
interest rate models
·
stochastic algorithms in finance
The following invited
speakers will participate:
Invito
alla Finanza Matematica - June 4, morning session
Dott. Giovanni Andrea Adragna, TradingLab, Unicredito Italiano, Milano: Modelli
di finanza quantitativa nella pratica operativa di un desk (abstract)
Prof. Emilio Barucci, Dip. di Statistica e Matematica applicata
all’Economia, Università di Pisa: The informational role of prices:
theory and empirical implications (abstract)
Prof. Paolo Guasoni, Dip. di
Matematica, Università di Pisa: Investire in un mercato inefficiente
(abstract)
Lectures
on Mathematical Finance - June 4, afternoon session
Prof. Tomas Björk, Dept. of Finance, Stockholm School
of Economics: Towards a General Theory of Good Deal Bounds (abstract)
Prof. Damien Lamberton, Lab. d’Analyse et Mathematiques
Appliquees, Université de Marne-la-Vallée, Paris: The two armed bandid in
finance (abstract)
Prof. Claudia Klüppelberg, Center for Mathematical Sciences,
Munich University of Technology: A Continuous Time GARCH Process Driven
by a Lévy Process: Stationarity and Second Order Behaviour (abstract)
Prof. Arturo Kohatsu Higa, Dept.of
Economics and Business, Universitat Paompeu Fabra, Barcelona: Examples of
insider models (abstract)
You can find available online: the
program [click HERE] and
the (preliminary) list of participants [click HERE].
No registration fee is requested but, please, register your
participation by sending an e-mail including name, affiliation and e-mail
address to
If you like, you can visit the web pages
of the past three editions: l’Aquila in
2003, Pescara
in 2002 and Roma
Tre in 2001.
For information about:
hotels in Rome: see the website
http://www.venere.com/it/roma/index.html.en;
how to reach the department: visit its website http://www.mat.uniroma2.it/
(in
particular, see http://www.mat.uniroma2.it/e-coord.htm)
For futher information, please contact the organizers:
Fabio Antonelli (antonf@univaq.it)
Paolo
Baldi (baldi@mat.uniroma2.it)
Sergio
Scarlatti (scarlatt@sci.unich.it)
Giovanni Andrea Adragna
Modelli di finanza quantitativa nella pratica operativa
di un desk
TradingLab, Unicredito Italiano,
Milano
mailto:GiovanniAndrea.Adragna@tradinglab.unicredit.it
Verranno descritti i 4 principali apparati della
banca ai quali trovano accesso laureati/dottorati nelle discipline
Matematica-Fisica-Ingegneria. Questi sono: Front Office, Risk Management,
Financial Modeling, Information Technology. Per ciascuna delle aree esaminate
verranno esposte attività quotidiane e straordinarie, livelli di
responsabilità, requisiti tecnici e possibili carriere.
(back)
Tomas Björk
Towards a General Theory of Good Deal Bounds
Dept. of
Finance, Stockholm School of Economics
We consider a Markovian factor model consisting
of a vector price process for traded assets as well as a multidimensional
random process for non traded factors.
All processes are allowed to be driven by a general marked point process
(representing discrete jump events) as
well as by a standard multidimensional standard Wiener process. Within this
framework we provide the following results.
1. We extend the Hansen-Jagannathan bounds for
the Sharpe Ratio to the point process setting.
2. We study arbitrage free good deal pricing
bounds for derivative assets along the lines of Cochrane and Saa-Requejo. Using
martingale techniques we derive the relevant Hamilton-Jacobi-Bellman equation
for the upper and lower good deal bound functions, thus extending the results
from Cochrane and Saa-Requejo to the point process case.
3. In
particular we study the case of a single price process driven by a scalar
Wiener process as well as by a marked point
process. For this case we provide a detailed analysis of the dynamic
programming equation and the optimal market prices of risk. As a concrete
application we present numerical results for the classic Merton jump-diffusion
model.
(back)
Paolo Guasoni
Investire in un mercato inefficiente
Dipartimento di Matematica,
Università di Pisa
In genere un mercato viene definito efficiente
quando "i prezzi riflettono pienamente l'informazione disponibile"
(Fama, 1970) e i rendimenti attesi sono costanti. Gli esempi piu' tipici di
mercati efficienti sono i modelli basati su passeggiate aleatorie e moto
Browniano. Se si lascia cadere l'ipotesi di rendimenti attesi costanti, si
ottengono modelli in cui gli agenti hanno la possibilita' di prevedere in modo
non banale i rendimenti futuri, pur non potendo realizzare arbitraggi.
In questo seminario verra' studiato un modello
introdotto da Shiller (1984) e Summers (1986), in cui le variazioni dei prezzi
includono sia una componente persistente (razionale) che una temporanea
(irrazionale). Verra' studiato il problema di investimento ottimale prima per
un agente economico informato, che osserva sia il valore di mercato che il
valore fondamentale, poi per un agente disinformato, che osserva solo il valore
di mercato. Per l'agente informato il processo dei prezzi e' Markoviano, quindi
le decisioni di investimento richiedono solo la conoscenza dei valori odierni,
mentre per l'agente disinformato la strategia ottimale richiede l'utilizzo di
tutta la storia passata dei prezzi.
(back)
Claudia
Klüppelberg
A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity
and Second Order Behaviour
Center for Mathematical Sciences, Munich University of Technology
We use a discrete time analysis, giving
necessary and sufficient conditions for the almost sure convergence of ARCH(1)
and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH
concept to continuous time processes. Our ``COGARCH" (continuous time
GARCH) model, based on a single background driving L\'evy process, is different
from, though related to, other continuous time stochastic volatility models
that have been proposed. The model generalises the essential features of
discrete time GARCH processes, and is amenable to further analysis, possessing
useful Markovian and stationarity properties.
This is joint work with Alexander Lindner and
Ross Maller.
(back)
Arturo Kohatsu Higa
Examples of insider models
Dept.of
Economics and Business, Universitat Paompeu Fabra, Barcelona
In this talk mostly directed to young researchers
and PhD students we will introduce the most significative examples in models
for insider trading. We will consider various issues time permitting. We will
consider:
1. Insider trading in Brownian environment.
This is the most considered model which postulates that stock prices are
determined by small investors and the
insider has future information not available to the small investors.
2. Insider trading in markets with jumps. One
drawback of the model(s) in 1. is that optimal trades of insiders are highly
oscillating. One way of solving this problem is to consider markets with jumps.
3. Models of the stock price for the insider.
Here we consider an insider that has an effect of the stock price as regarded
by the small investor. This uses anticipating calculus techniques.
(back)
Damien Lamberton
The two armed bandid in finance
Lab. d’Analyse et
Mathematiques Appliquees, Université de Marne-la-Vallée, Paris
This talk is based on joint work with Gilles
Pagès and Pierre Tarrèes. We investigate the asymptotic behaviour of the so-called
two-armed bandit algorithm and describe en application to asset allocation. We
show that the convergence of the algorithm to the desired limit may fail to
occur for some values of the parameters. We also give a sufficient condition
for convergence to the good limit.
(back)