Market arbitrage versus agent arbitrage

The present paper provides conditions for the consistency among different orderings which may be defined on sets of financial portfolios; in particular, a different reading key for some classical results is proposed. Besides arbitrage (whose impossibility is necessary and sufficient for consistency between the orderings based on prices and payoffs, respectively), a different notion, the agent arbitrage, is introduced. It turns out to be useful to enlighten links among orderings: in particular, no agent arbitrage embodies the equivalence between the preorder induced by prices and the one induced by agent's utility.