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<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Inoltro avviso
di Seminario a me pervenuto.</EM></FONT></DIV>
<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Cordiali
saluti</EM></FONT></DIV>
<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Liviana
Paoletti</EM></FONT></DIV>
<DIV> </DIV></FONT></DIV></FONT></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=verde@sns.it href="mailto:verde@sns.it">Michele VERDE - Scuola Normale
Superiore di Pisa</A> </DIV>
<DIV><B>To:</B> <A title=docenti.scienze@sns.it
href="mailto:docenti.scienze@sns.it">Docenti Scienze</A> ; <A
title=ricercatori.scienze@sns.it
href="mailto:ricercatori.scienze@sns.it">Ricercatori Scienze</A> ; <A
title=perfezionandi.scienze@sns.it
href="mailto:perfezionandi.scienze@sns.it">Perfezionandi Scienze</A> ; <A
title=studenti.scienze@sns.it href="mailto:studenti.scienze@sns.it">Studenti
Scienze</A> ; <A title=borsisti.scienze@sns.it
href="mailto:borsisti.scienze@sns.it">Borsisti Scienze</A> </DIV>
<DIV><B>Cc:</B> <A title=sitosns@sns.it href="mailto:sitosns@sns.it">Sito
SNS</A> ; <A title=paoletti@dm.unipi.it
href="mailto:paoletti@dm.unipi.it">Liviana Paoletti</A> ; <A
title=curciare@dm.unipi.it href="mailto:curciare@dm.unipi.it">Curciarello Giulia
- Dip.mat.Tonelli</A> ; <A title=laspina@dm.unipi.it
href="mailto:laspina@dm.unipi.it">Alessandra La Spina</A> </DIV>
<DIV><B>Sent:</B> Tuesday, May 04, 2010 9:23 AM</DIV>
<DIV><B>Subject:</B> Avviso seminario di Finanza Matematica, prof. Fausto GOZZI
(06.05.10)</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman'"><STRONG><U>SEMINARIO DI
<SPAN style="mso-no-proof: yes">FINANZA
MATEMATICA</SPAN><o:p></o:p></U></STRONG></SPAN></P>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'"><o:p><SPAN
style="TEXT-DECORATION: none"><STRONG><U></U></STRONG></SPAN></o:p></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes"></SPAN> </H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">giovedì 6 maggio
2010</SPAN><SPAN style="FONT-FAMILY: 'Times New Roman'"><o:p></o:p></SPAN></H2>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9.05pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">ore
11<SPAN style="mso-no-proof: yes">.30</SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9.05pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'"><o:p> </o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><U><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">Pisa<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">(Aula
<SPAN style="mso-no-proof: yes">Bianchi</SPAN>)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><B><U><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'"><o:p><SPAN
style="TEXT-DECORATION: none"></SPAN></o:p></SPAN></U></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes"></SPAN></I></B> </P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">Fausto
GOZZI<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">Luiss,
Roma</SPAN></I><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'"><o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN style="FONT-FAMILY: 'Times New Roman'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">Terrà<SPAN
style="mso-spacerun: yes"> </SPAN>un seminario dal
titolo:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><SPAN
style="FONT-FAMILY: 'Times New Roman'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">“<SPAN
style="mso-no-proof: yes">Assel Liabilit Management for Pension Funds: a
Stochastic Control Approach</SPAN>”<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">Abstract<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">In
this talk we propose and study a continuous time stochastic model of optimal
allocation for a defined contribution pension fund with a minimum guarantee. We
adopt the point of view of a fund manager maximizing the expected utility from
the fund wealth over an infinite horizon.<o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">In
our model the dynamics of wealth takes directly into account the flows of
contributions and benefits and the level of wealth is constrained to stay above
a ``solvency level''. The fund manager can invest in a riskless asset and in a
risky asset but borrowing and short selling are prohibited. The model is
naturally formulated as an optimal stochastic control problem that have some
similarities with similar to Merton's optimal portfolio
problems.<o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">The
main technical issues that render this problem difficult are:- the presence of
state constraints, motivated by the prescription of the "solvency level".- the
presence of delay terms (the so-called "surplus") in the state equation, due to
the standard form of the contract (the pension give to the subscribers depends
on the past performance of the fund).<o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">First
we concentrate first the analysis on the effect of the solvency constraint,
analyzing in particular what happens when the fund wealth reaches the allowed
minimum value represented by the solvency level. Here we show that the value
function of the problem is a regular solution of the associated
Hamilton-Jacobi-Bellman equation. Then we apply verification techniques to get
the optimal allocation strategy in feedback form and to study its properties. We
finally give a special example with explicit solution.<o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">Second
we consider the problem where also the "surplus" is present. This problem is
naturally infinite dimensional and is much more difficult. We present here the
ideas used to approach it and some first partial results.</SPAN></I><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">Tutti gli interessati
sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'"><o:p> </o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2">
</SPAN>SAD<o:p></o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><FONT
face="Times New Roman"><SPAN lang=EN-GB><SPAN style="mso-tab-count: 2"><FONT
size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: IT">Classe
di Scienze</SPAN></FONT><SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: IT"><o:p></o:p></SPAN></P></FONT></DIV>
<DIV><FONT face=Arial size=2>- - - - -<BR>Michele VERDE<BR>Scuola Normale
Superiore<BR>Servizio Supporto Attività Didattiche - Scienze<BR>Piazza Dei
Cavalieri, 7<BR>I - 56126 Pisa</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Tel. 050-509048<BR>Fax. 050-509045<BR>E-Mail: <A
href="mailto:m.verde@sns.it">m.verde@sns.it</A><BR>E-Mail: <A
href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</A><BR>- - - -
-</FONT></DIV>
<DIV> </DIV>
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