---------- 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 ------- End of forwarded message -------