---------- Forwarded message ----------
Date sent: Fri, 21 Mar 2003 11:30:23 +0100 (CET)
From: Marzia De Donno <mdedonno(a)dm.unipi.it>
Subject: cattedra galileiana 2003
Scuola Normale Superiore
Associazione Amici
della
Scuola Normale Superiore
Cattedra Galileiana 2003
Halil Mete Soner
Koc University
Istanbul, Turkey
A course on:
Stochastic Optimal Control Methods In Finance
April 7th - May 6th, 2003
Abstract: Stochastic optimal control methods have been extensively
used in financial economics since the pioneering work of Merton on
optimal consumption and investment. Stochastic optimal control is a
powerful tool as it provides dynamic investment and consumption
strategies in a systematic manner. In the Merton framework, financial
market is a complete one and the resulting optimal control problem fit
into the classical framework. However, in the case of market
incompleteness or friction, we encounter interesting control problems.
The model with transaction costs is an important example. This model
was first introduced by Constantinides and later studied by Davis &
Norman, is a singular stochastic model. It is related to the monotone
follower problems studied in the control literature by Karatzas &
Shreve and Shreve & Soner.
In the presence of market friction or incompleteness, optimal control
also provides alternate approaches for pricing derivative securities.
One of these is the idea of super-replication and the other is to
introduce preferences through a utility function. Both of these
approaches coincide with the classical no-arbitrage price in complete
markets.
In these lectures, we outline the recent developments in finance and
stochastic optimal control that are related. Problems with "singular"
models and the super-replication problem will be emphasized.
Mathematically, we will use the theory of viscosity solutions to
analyze the resulting nonlinear partial differential equations.
Also, we will outline a connection between geometric flows and
super-replication problems.
Lectures will be given at the "Sala degli Stemmi" Scuola Normale
Superiore di Pisa, according to the following schedule.
Monday, April 7th - 15:00-17:30
Lecture 1. Optimal control and viscosity solution. This is a general
introduction to stochastic optimal control, dynamic programming,
dynamic programming equation and viscosity solutions.
Tuesday, April 8th -10:00-12:30
Lecture 2. Singular stochastic control. These are optimal control
problems in which the state process can move discontinuously in time.
We will provide a general framework and discuss models with
transaction costs.
Monday, April 14th -15:00-17:30
Lecture 3. Super-replication. General target problems will be
introduced and the super-replication will be discussed.
Tuesday, April 15th -10:00-12:30
Lecture 4. Pricing with Portfolio Constraints. Super-replication with
portfolio constraints will be studied first by convex duality of
Cvitanic & Karatzas and Karatzas & Kuo. Then, we will use the target
control problem techniques of Soner & Touzi.
Monday, April 28th -15:00-17:30
Tuesday, April 29th - 10:00-12:30
Lectures 5 and 6. Gamma Constraints. We discuss the problem of pricing
under a constraint on the variations of the portfolio. Several
probabilistic results on double stochastic integrals and PDE results
on non-parabolic equations will be given.
Monday, May 5th - 15:00-17:30
Tuesday, May 6th - 10:00-12:30
Lectures 7 and 8. Geometric flows, super-replication, and finance. A
general study of super-replication, or more generally the target
control problem, yields geometric equations. Particular choices of the
target problems provide a stochastic representation for mean curvature
flow and other important parabolic geometric flows.
Registration
The participation to the course is open but registration is needed.
Thus, the registration form below should be completed and sent by fax,
mail or e-mail to:
Associazione Amici della
Scuola Normale Superiore
Piazza dei Cavalieri 7 - 56126 PISA
Tel. (+39) 050 509 654; fax: (+39) 050 509 534
Pag. web:
http://www.sns.it/Home/Associazione_Amici_della_Normale/cgal.html
E_mail: amicisns(a)sns.it
Registration Form
Name:
Surname:
Professional status:
Affilation:
Address, Tel./Fax: _______________________
__________________________________________
E-mail: __________________________________
dott.ssa Gisella Chinè
Associazione Amici della Scuola Normale Superiore
Piazza dei Cavalieri 7 - 56126 Pisa
Tel. +39 050 509.654 - fax +39 050 509.534
http://www.sns.it/~Amici_della_Normale
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