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 well-defined maximum which can be achieved in full knowledge of the distribution of the entire process. The fundamental limits reveal that the so-called log-optimal portfolio is the best possible choice.