Before revision:  This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes  .
After revision: The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a benchmark portfolio over a given time-horizon with probability one. This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes .