  We design an optimal strategy for investment in a portfolio of assets subject
to a multiplicative Brownian motion. The strategy provides the maximal typical
long-term growth rate of investor's capital. We determine the optimal fraction
of capital that an investor should keep in risky assets as well as weights of
different assets in an optimal portfolio. In this approach both average return
and volatility of an asset are relevant indicators determining its optimal
weight. Our results are particularly relevant for very risky assets when
traditional continuous-time Gaussian portfolio theories are no longer
applicable.

Statistical Mechanics;Disordered Systems and Neural Networks;Portfolio Management