we treat the question of whether asset prices admit a martingale measure when the markets are free of arbitrage opportunities. The arbitrage opportunities we consider are restricted to originate from simple trading strategies, which are most closely related to actual market portfolios. It is shown that if such simple arbitrage profits are excluded, then indeed a martingale measure exists. Nevertheless it will in general lack regularity properties and pricing bubbles may arise. The Fundamental Theorem of Asset Pricing may also be proved based solely on simple processes but the usual reiforcement of the notion of arbitrage is needed.