Absence of arbitrage in markets with infinitely many assets (Q2740095)

The author considers two notions of absence of arbitrage for one-period models of markets with infinitely many assets. The strict arbitrage corresponds to making a profit without risk, whereas the approximate arbitrage is making a profit with arbitrarily small risk. The author proves the equivalence between the absence of approximate arbitrage and the conditions of continuity of the cost functional and absence of strict arbitrage.