Before revision:  The main result consists in a proof of  existence and uniqueness of a strategy, called relatively growth optimal, such that the logarithm of the share of its wealth in the total wealth of the market is a submartingale for any strategies of the other investors.
After revision:  The main result consists in a proof of the existence and uniqueness of a strategy, called relatively growth optimal, such that the logarithm of the share of its wealth in the total wealth of the market is a submartingale for any strategies of the other investors.