<html><head><title>cgal3- "Amici della Scuola Normale"</title></head>
<body alink="#871a24" vlink="#999900" link="#712004" text="#083d07" background="cgal3_files/sfondo1.jpg">
<center><table width="40%">
<tbody><tr>
<td align="center"><img alt="stemma della Sc. Normale Superiore" width="45" height="69" src="cgal3_files/stemma1.gif"></td>
<td align="center"><font face="times" size="+1"><b>Cattedra Galileiana </b></font></td>
</tr>
</tbody></table></center>
<p align="center" class="MsoNormal"><span lang="EN-US"><font size="4"> </font></span></p>
<p align="center" class="MsoNormal"> </p>
<p align="center" style="" class="MsoNormal">
<span lang="EN-US" style="font-size: 13.5pt;"> </span>
<span lang="EN-US">
<b><font size="5">C</font></b><font size="5">attedra</font><font size="5"> <b>G</b>alileiana
13 - 1</font></span><font size="5">7<span lang="EN-US">
settembre 2004</span></font></p>
<p style="" class="MsoNormal"> </p>
<p style="" class="MsoNormal"><span lang="EN-US" style="">From September 13 to 1</span><span style="">7</span><span lang="EN-US" style=""> Scuola Normale Superiore will host two courses of the Cattedra Galileiana
series: </span></p>
<p style="" class="MsoNormal"><b><span lang="EN-US" style="">Prof. Nicole EL KAROUI</span></b><span lang="EN-US" style="">
(Ecole Polythecnique, Palaiseau Francia)<br>
<i style="">Lectures on Optimal Stopping problems and Non-linear Representations</i>
</span></p>
<p class="MsoNormal"><span lang="EN-US" style="">Optimal stopping problems have
received renewed interest with the theory of American Options in Finance or Real
options in Economics. While the theory is well-established since the Sixties,
new developments are proposed in view of more efficient computational methods of
the optimal stopping time: quasi-explicit formulae, free boundary, Monte-Carlo
methods... </span></p>
<p class="MsoNormal"><span lang="EN-US" style="">More recently, motivated by the
Bandit problems or Optimal consumption plan with habit formation problem, a
non-linear representation of processes or supermartingale has been introduced.
All these representations are given in terms of the conditional expectation of
the running supremum of an index process that we characterize. Take the running
supremum of a process may be interpreted in the Max-plus Algebra $R^{\rm max}$
(where the two algebraic operations are $\oplus={\rm max}$ in place of $+$, and
$\otimes=+$ in place of $\star$), as an integral. Some applications of these new
decompositions are proposed. </span></p>
<ol>
<li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">Some
explicit examples of optimal stopping problems: American options with infinite
horizon, Options on the maximum (Russian options) and other options from G.
Peskir and A. Shyraev.</span><span lang="EN-US"> </span>
</p></li><li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">
Optimal Stopping and Reflected Backward Stochastic Differential equations from
NEK, Pardoux, Peng, Quenez.</span><span lang="EN-US"> </span>
</p></li><li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">
General Theory of the optimal stopping problem: problems related to the jumps
from Cours de Saint- Flour...</span>
</p></li><li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">
<st1:place>Monte Carlo</st1:place> methods in solving optimal stopping</span><span style="">.</span><span lang="EN-US" style="">
Problems: Longstaff and Schwarz Algorithm and extensions.</span><span lang="EN-US">
</span>
</p></li><li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">Non
linear representation in the Max-Plus Algebra</span><span style=""> </span>
<span lang="EN-US" style="">from P.Bank, H.Foellmer, NEK</span><span lang="EN-US">
</span>
</p></li><li>
<p style="margin-top: 0pt; margin-bottom: 0pt;"><span lang="EN-US" style="">
Applications to American options, American Guaranteed, and stochastic order.</span><span lang="EN-US">
</span>
</p></li></ol>
<p><><span lang="EN-US" style=""> </span></> </p>
<p class="MsoNormal"><b><span lang="EN-US" style="">Prof. Dmitry KRAMKOV </span>
</b><span lang="EN-US" style="">(<st1:place>
<st1:placename>Carnegie</st1:placename>
<st1:placename>Mellon</st1:placename>
<st1:placetype>University</st1:placetype> </st1:place>
,
<st1:city>
<st1:place>Pittsburg</st1:place> </st1:city>
) </span></p>
<p style="word-spacing: 0px;" class="MsoNormal"><i><span lang="EN-US" style="">
Utility based valuation in incomplete markets </span></i></p>
<p class="MsoNormal"></p>
<p style="text-align: justify;" class="MsoNormal"><b style="">Abstract:<span style="">
<br>
</span></b>As it is well known, in a complete financial market every contingent
claim can be perfectly replicated by a controlled portfolio of the traded
securities and therefore admits a well-defined arbitrage-free price.<span style="">
</span>In an incomplete market, to every contingent claim is associated an
interval of arbitrage-free prices. In this case, in order to determine a unique
price arbitrage arguments alone are not, in general, sufficient and the
preferences of the economic agent under consideration should be taken into
account.</p>
<p style="text-align: justify;" class="MsoNormal">The goal of the course is to
present some recent results related to the theory of utility based pricing in
incomplete markets, where the preferences of the investor are modeled, as it is
usual in economic theory, through the expected utility of terminal wealth. The
main emphasis will be on mathematical aspects of the problem such as the
formulation of precise or at least sufficiently sharp conditions for the key
assertions of the theory to hold true. The course will be based on joint papers
with Walter Schachermayer, Julien Hogonnier and Mihai Sirbu.</p>
<ol>
<li><span lang="EN-US" style=""><span style="font-style: italic;">Overview of
arbitrage-free pricing.</span><br>
We introduce the general semimartingale model for financial market. We define
the concept of arbitrage-free price and formulate the first and the second
fundamental theorems of asset pricing. Finally, we present results related to
replication and super-hedging of contingent claims and derive bounds for
arbitrage-free prices of derivatives.</span></li>
<li><span lang="EN-US" style=""><span style="font-style: italic;">Optimal
investment in incomplete markets.</span><br>
We present a careful mathematical study of the problem of expected utility
maximization. The main emphasis will be on “qualitative” properties such as
the existence of the optimal investment strategy, two-times differentiability
of the value function and so on. The results presented in this part will
form a foundation for the future analysis of utility based prices.</span></li>
<li><span lang="EN-US" style=""><span style="font-style: italic;">Optimal
investment with random endowments. </span><br>
We study the problem of expected utility maximization for an economic agent
who, in addition to an initial capital, receives random endowments at
maturity. We show that an appropriate choice of the variables of the
optimization problem can significantly simplify the study of the duality
relations.</span></li>
<li><span lang="EN-US" style=""><span style="font-style: italic;">Sensitivity
analysis of utility based prices. </span><br>
We present asymptotic analysis of utility based prices with respect to “small”
number of non-traded contingent claims. In particular, we show that the
asymptotic analysis captures some important “qualitative” properties of these
prices if and only if there is a risk-tolerance wealth process. </span></li>
</ol>
<p>Moreover, some semirars will be held by Professors <span lang="EN-US">Rama Cont, Helyette Geman, Huyen Pham, and Wolfgang Runggaldier. </span>
</p>
<p> </p>
<p style="" class="MsoNormal"><span lang="EN-US" style=""><br>
The lectures </span><span style="">and the semirars </span><span lang="EN-US" style="">will take place at Scuola Normale Superiore (Aula U. Dini, Palazzo
Castelletto) with the following schedule: </span></p>
<table height="269" width="435" cellspacing="0" cellpadding="0" border="1" style="border: medium none ; border-collapse: collapse;">
<tbody><tr style="">
<td height="16" valign="top" style="border: 0.5pt solid windowtext; padding: 0cm 5.4pt; width: 113px;">
<p style="word-spacing: 0px;" class="MsoNormal">13 Mo<span lang="EN-US" style="">nday</span></p></td>
<td height="16" valign="top" style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 0.5pt 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 95px;">
<p class="MsoNormal">15.00-16.30<br>
17.00-18.30<br>
</p></td>
<td height="16" valign="top" style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 0.5pt 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 181px;">
<p class="MsoNormal">El Karoui<br>
Kramkov<br>
</p></td>
</tr>
<tr style="">
<td height="56" valign="top" style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 0.5pt 0.5pt; padding: 0cm 5.4pt; width: 113px;">
<p class="MsoNormal">14 Tuesday</p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 95px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
10.00-11.30</p>
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
15.00-16.30</p><p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
17.00-18.30</p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 181px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">El Karoui<br>
Kramkov</p><p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">El
Karoui</p></td>
</tr>
<tr style="">
<td height="56" valign="top" style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 0.5pt 0.5pt; padding: 0cm 5.4pt; width: 113px;">
<p class="MsoNormal">15 Wed<span lang="EN-US" style="">nesday</span></p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 95px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
10.00-11.30</p>
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
15.00-16.30</p><p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
17.00-18.30</p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 181px;">
<p class="MsoNormal">Kramkov<br>
El Karoui<br>
Kramkov</p></td>
</tr>
<tr style="">
<td height="75" valign="top" style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 0.5pt 0.5pt; padding: 0cm 5.4pt; width: 113px;">
<p class="MsoNormal">16 Thursday</p></td>
<td height="75" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 95px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal"> 9.00-10.30</p>
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
11.00-12.00<br>
15.00-16.30<br>
17.00-18.00</p></td>
<td height="75" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 181px;">
<p class="MsoNormal">El Karoui<br>
Seminar: H. Pham<br>
Kramkov<br>
Seminar: W. <span lang="EN-US">Runggaldier</span></p></td>
</tr>
<tr style="">
<td height="56" valign="top" style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 0.5pt 0.5pt; padding: 0cm 5.4pt; width: 113px;">
<p class="MsoNormal">17 Friday</p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 95px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal"> 9.00-10.30<br>
11.00-12.30</p>
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
15.00-16.00</p><p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
16.15-17.15</p></td>
<td height="56" valign="top" style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 0.5pt 0.5pt medium; padding: 0cm 5.4pt; width: 181px;">
<p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">El Karoui<br>
Kramkov<br>
Semi<span lang="EN-US" style="">nar</span><span style="">: </span>H. Geman</p><p style="margin-top: 0pt; margin-bottom: 0pt;" class="MsoNormal">
Seminar: R. Cont</p></td>
</tr>
</tbody></table>
<p class="MsoNormal"><span lang="EN-US" style=""> </span></p>
<p class="MsoNormal"><span lang="EN-US" style=""> Practical information on
travel and accommodation in
<st1:city>
<st1:place>Pisa</st1:place> </st1:city>
can be found at <a href="http://www.crm.sns.it/info.html">
http://www.crm.sns.it/info.html</a> </span></p>
<h1 align="center" style="text-align: center;">
<span lang="EN-GB" style="font-size: 10pt; font-family: Palatino;"> </span>
<span lang="EN-US" style="font-size: 13.5pt; font-family: Times;">R</span><span lang="EN-US" style="font-size: 10pt; font-family: Times;">egistration:</span><span lang="EN-GB" style="font-size: 10pt; font-family: Palatino;">
</span></h1>
<p style="" class="MsoNormal"><span lang="EN-US" style="">Participation is free, and
meals will be offered to registered participants by Associazione Amici della
Scuola Normale Superiore.<br>
To register, send an e-mail to (</span><span lang="EN-US" class="MsoHyperlink" style="color: navy; text-decoration: none;"><a href="mailto:amicisns@sns.it"><span style="color: rgb(113, 32, 4);">amicisns@sns.it</span></a></span><span lang="EN-US" style="">)
with the following information: </span></p>
<p align="center" style="text-align: center;">
<span lang="EN-US" style="font-size: 10pt; font-family: Times;">Registration
Form<br>
Name ___________________________________________<br>
<br>
Surname _________________________________________<br>
<br>
Professional Status _________________________________<br>
<br>
Affilation ________________________________________<br>
<br>
Address _________________________________________<br>
<br>
Telephone__________________ Fax __________________<br>
<br>
E-mail __________________________________________<br>
<br>
Date ___________________________________________<br>
<span style=""> </span> </span></p>
<p align="center"><font size="-1" face="times"> </font></p>
<p align="center"><font size="-1" face="times"><i>
<a href="http://www.sns.it/Home/amici-word/2004/cgal_sett_04/cgal4.html">Cattedra Galileiana</a>
<a href="http://www.sns.it/Home/amici-word/2004/cgal_sett_04/nov.html">Novità</a></i></font></p>
<hr width="15%">
<p align="center"><font size="-2" face="times">Per informazioni:<br>
Associazione Amici della Scuola Normale Superiore <br>
Piazza dei Cavalieri, 7 - 56126 Pisa<br>
Tel. 050/509.654 - Fax 050/509.534<br>
<a href="mailto:%20amicisns@sns.it">E-mail: amicisns@sns.it</a></font></p>
<p align="center" style="" class="MsoNormal"><span style="font-size: 13.5pt;" lang="EN-US"> </span></p>
<font face="times" size="-1">
</font><p align="center"><font face="times" size="-1"> </font></p>
<p align="center"><font face="times" size="-1"><font face="times" size="-1"><i><a href="http://www.sns.it/Home/Associazione_Amici_della_Normale/cgal4.html">Cattedra Galileiana</a>
<a href="http://www.sns.it/Home/Associazione_Amici_della_Normale/nov.html">Novità</a></i></font></font></p>
<font face="times" size="-1">
</font><hr width="15%">
<p align="center"><font face="times" size="-1"><font face="times" size="-2">Per informazioni:<br>
Associazione Amici della Scuola Normale Superiore <br> Piazza dei Cavalieri, 7 - 56126 Pisa<br>
Tel. 050/509.654 - Fax 050/509.534<br>
<a href="mailto:%20amicisns@sns.it">E-mail: amicisns@sns.it</a></font></font></p>
</body></html>