  We propose a multi-agent model of an asset market and study conditions that
guarantee that the strategy of an individual agent cannot outperform the
market. The model assumes a mean-field approximation of the market by
considering an infinite number of infinitesimal agents who use the same
strategy and another infinitesimal agent with a different strategy who tries to
outperform the market. We show that the optimal strategy for the market agents
is to split their investment budgets among the assets proportionally to their
discounted expected relative dividend intensities.
