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INVITO ALLA FINANZA MATEMATICAand LECTURES ON MATHEMATICAL FINANCE Rome, June 4, 2004
Programme
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INVITO ALLA FINANZA MATEMATICA
9:50- 10:00 Presentazione agli studenti
10.00-10:45 E. Barucci: “The informational role of prices: theory
and empirical implications”
10.45-11.30 G. A. Adragna: “Modelli
di finanza quantitativa nella pratica operativa di un desk”
Abstract. 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.
11.30-12.00 Pausa
12.00-12.45 P. Guasoni: “Investire in un mercato inefficiente”
Abstract. 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.
LECTURES
ON MATHEMATICAL FINANCE
14:20-14:30: Opening
14.30-15.30 T. Björk: “Towards a General Theory of Good Deal
Bounds”
Abstract. 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.
15.30-16.30 A. Kohatsu-Higa: “Examples of insider
models”
Abstract. 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.
16.30-17.00 Coffee break
17.00-18.00 D. Lamberton: “The two armed bandid in finance”
Abstract. 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.
18.00-19.00 C. Klüppelberg: “A Continuous Time GARCH Process
Driven by a Lévy Process:
Stationarity and Second Order Behaviour”
Abstract. 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.
19.00-19.05 Closing
20:30 Social Dinner