---------- 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} ---------------------------------------------------------- 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 -----------------------------------------------------------