Financial and Actuarial Mathematics: Time Table
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TOMORROW:
PV Schachermayer (Tuesday 16:30-18:00, TU FH, Turm A, 6. Stock, SR 107)
23.01.2001 - Eva Strasser:
Change of Numeraire and the Numeraire Portfolioin Financial Models
Abstract:
In my master thesis, I consider market models consisting of finitely many
assets, which are modeled by continuous semimartingales. A numeraire is
a strictly positive security, e.g. a fixed-interest security or, more
generally, any security modeled by a strictly positive semimartingale.
A tradable numeraire is any strictly positive, continuous semimartingale
attainable in the market.
One of the aims in my master thesis is to analyse the effects of a change
of numeraire on the most important properties of a market model. Another
important topic is the so-called numeraire portfolio, which is a special
case of an inverse local martingale density. A main result of my master
thesis is an existence criterion for the numeraire portfolio. It turns out
that a certain structure condition of the market is necessary and
sufficient for the existence of the numeraire portfolio. This result is
based on the basic existence criterion for local martingale densities by
Schweizer (1994). Moreover, I discuss some properties of the numeraire
portfolio along the line of Becherer (1999).
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SE Schachermayer (Thursday 16:30-18:00; TU FH, Turm A, 6. Stock, SR 107)
25.01.2001 - A.V. Nagaev (Nicolaus Copernicus University of Torun):
On an optimal choice a European option
Abstract:
A discrete time model of financial market is considered. It is assumed
that only two types of securities, risky and non-risky, are circulated.
In the focus of attention is the question how to choose "better" option.
The stated fair play principle aims to protect to some extent the client
interests. The principle allows one to characterize the quality of
option by a functional and, therefore, to state correctly a problem of
optimization. The developed theory is of interest. It is illustrated by
an experiment implemented on the basis of real data.
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See also:
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