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BEGIN:VEVENT
DTSTAMP:20191115T122221Z
DTSTART:20191118T150000Z
DTEND:20191118T160000Z
SUMMARY:Igor Evstigneev (Manchester) - Von Neumann-Gale dynamical system
s and their applications
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}bt-k30445h3
-8ofq5q
DESCRIPTION:Igor Evstigneev (Economics Department\, University of Manches
ter) will be speaking at this research seminar\, part of the Dynamical S
ystems and Analysis seminar series. \n\nAbstract: Von Neumann-Gale dynam
ical systems are defined in terms of multivalued operators possessing pr
operties of convexity and homogeneity. These operators assign to each el
ement of a given cone a convex subset of the cone describing possible on
e-step transitions from one state of the system to another. The classica
l\, deterministic theory of such dynamics was originally aimed at the mo
delling of economic growth (von Neumann 1937 and Gale 1956). Key results
on von Neumann-Gale dynamical systems may be regarded as multivalued no
nlinear versions of the Perron-Frobenius theorem on eigenvectors and eig
envalues of positive matrices. First attempts to build a stochastic gene
ralization of this theory were undertaken in the 1970s by Dynkin\, Radne
r and their research groups. However\, the initial attack on the problem
left many questions unanswered. Substantial progress was made only in t
he late 1990s\, and final solutions to the main open problems were obtai
ned only in the last decade. At about the same time it was observed that
stochastic analogues of von Neumann-Gale dynamical systems provide a na
tural and convenient framework for financial modelling (asset pricing an
d hedging under transaction costs). This observation gave a new momentum
to studies in the field and posed interesting new questions. The talk w
ill review this area of research\, emphasising recent achievements relat
ed to mathematical finance. \n\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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