Professor Eckhard Platen from University of Technology Sydney is giving a
VGSF research seminar on "A Benchmark Approach to Finance" on Thursday,
October 25, from 15:30 to 17:00 at Wirtschaftsuniversität Wien, HS D204
(UZA4, Nordbergstraße 15, 1090 Vienna). See the VGSF webpage (Activities &
Events --> Research Seminars) for the paper to download.
Please note the change of the time and location for this seminar!!!
The paper's abstract is attached below.
Best,
Youchang Wu
This paper derives a unified framework for portfolio optimization,
derivative pricing,
financial modeling, and risk measurement. It is based on the natural
assumption that
investors prefer more rather than less, in the sense that given two
portfolios with the
same diffusion coefficient value, the one with the higher drift is
preferred. Each such
investor is shown to hold an efficient portfolio in the sense of Markowitz
with units
in the market portfolio and the savings account. The market portfolio of
investable
wealth is shown to equal a combination of the growth optimal portfolio
(GOP) and
the savings account. In this setup the capital asset pricing model follows
without the use
of expected utility functions, Markovianity, or equilibrium assumptions.
The expected
increase of the discounted value of the GOP is shown to coincide with the
expected
increase of its discounted underlying value. The discounted GOP has the
dynamics of
a time transformed squared Bessel process of dimension four. The time
transformation
is given by the discounted underlying value of the GOP. The squared
volatility of the
GOP equals the discounted GOP drift, when expressed in units of the
discounted GOP.
Risk-neutral derivative pricing and actuarial pricing are generalized by
the fair pricing
concept, which uses the GOP as numeraire and the real-world probability
measure as
pricing measure. An equivalent risk-neutral martingale measure does not
exist under
the derived minimal market model.