From: Brenda Cook (brenda@math.missouri.edu)
Date: Mon Oct 16 2006 - 11:37:55 CDT
SPECIAL APPLIED MATH SEMINAR
University of Missouri-Columbia
Department of Mathematics
Igor Evstigneev
University of Manchester
Von Neumann-Gale Dynamical Systems with Applications in Economics and
Finance
Abstract: Von Neumann-Gale dynamical systems are defined in terms of
multivalued operators that possess certain properties of convexity and
homogeneity. These operators assign to each element of a given cone a
convex subset of the cone describing possible one-step transitions from
one state of the system to another. The classical, deterministic theory
of such dynamics was originally aimed at the modeling of economic growth
(von Neumann 1937 and Gale 1956). First attempts to build a stochastic
generalization of this theory were undertaken in the 1970s by Dynkin,
Radner and their research groups. However, the initial attack on the
problem left many questions unanswered. Substantial progress was made
only in the late 1990s. Recently it has been observed that stochastic
analogues of von Neumann-Gale systems provide a natural and convenient
framework for financial modeling (asset pricing and hedging under
transaction costs). This observation gave a new momentum to studies in
the field and posed new interesting questions. The talk will give an
introduction into the topic, review recent progress and discuss open
problems.
Friday, October 20, 2006
3:00-4:00 p.m.
312 Math Sciences
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