The purpose of this site is to collect results (papers, programs) of
Portfolio Group (László Györfi,
Gábor Gelencsér,
György Ottucsák, András Urbán and István
Vajda) at Budapest University of Technology and Economics
which are closely connected to sequential
investment strategies for financial markets.
Investment strategies
are allowed to use information collected from the past of the
market and determine, at the beginning of a trading period,
a portfolio, that is, a way to distribute their current
capital among the available assets. The goal of the investor
is to maximize his wealth on the long run without knowing the underlying
distribution generating the stock prices. Since accurate
statistical modeling of stock market behavior has been
known as a notoriously difficult problem, we take an
extreme point of view and work with minimal assumptions
on the distribution of the time series. In fact, the only
assumption that we use in our mathematical analysis is that
the daily price relatives form a stationary and ergodic
process. Under this assumption the asymptotic rate of growth
has a welldefined maximum which can be achieved in
full knowledge of the distribution of the entire process.
The fundamental limits
reveal that the socalled logoptimal portfolio is the
best possible choice.
