---------- Forwarded message ----------
From: Walter Schachermayer
---------- Forwarded message ----------
Date: Thu, 15 Dec 2005 11:26:57 -0300 (UYT)
From: Ernesto Mordecki <mordecki(a)cmat.edu.uy>
Subject: communications ICAM
Dear Collegues:
Time to submission of communications to ICAM 2006
is ending. We have two submissions (see below).
I think it is wise to wait a little more.
I asked for two collegues for submission here in the region,
and would like to know if you can help us to complete
the 4 or 5 communications, suggesting to some
collegues or students to participate.
There is information about support in
http://icam2006.cmm.uchile.cl/index.php
Best regards,
Ernesto
-------------------------------------
Pennanen Teemu -- Teemu . Pennanen @ hse . fi
Title:
Nonlinear price processes
Abstract:
This paper presents a stochastic model for trading in double auction
markets where the marginal cost of buying is a
nondecreasing function of the number of shares bought. The model admits a
generalized version of the fundamental theorem of
asset pricing.
------------------------------------------
\title{Convex Hedging in Incomplete Markets\\ and Generalizations}
\author{Birgit Rudloff, \\Martin-Luther-University Halle-Wittenberg, Germany}
In incomplete financial markets not every contingent claim can be
replicated by a self-financing strategy. The risk of the resulting
shortfall can be measured by convex risk measures. The dynamic
optimization problem of finding a self-financing strategy that
minimizes the convex risk of the shortfall can be split into a
static optimization problem and a representation problem. The
optimal strategy consists in superhedging the modified claim
$\widetilde{\varphi}H$, where $H$ is the payoff of the claim and
$\widetilde{\varphi}$ is the solution of the static optimization
problem, the optimal randomized test.
\\
In this talk, we will deduce necessary and sufficient optimality
conditions for the static problem using convex duality methods. We
deduce the dual problem and prove the validity of strong duality.
The solution of the static optimization problem turns out to be a
randomized test with a typical $0$-$1$-structure.
\\
The results can be generalized to solve the hedging problem for a
more general class of risk measure. Furthermore, we can apply
these results to the problem of testing compound hypothesis. This
extends previous results.
\end{document}
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Ernesto Mordecki
http://www.cmat.edu.uy/~mordecki mordecki(a)cmat.edu.uy
Postal Address: Facultad de Ciencias. Centro de Matematica
Igua 4225, C.P. 11400, Montevideo, Uruguay
Tel: (598 2) 525 25 22 Int. 122 Fax: (598 2) 522 06 53
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