A criterion for the absence of arbitrage in a discrete model of a securities market under convex portfolio constraints

In the case of a finite probability space, we obtain a criterion for the absence of arbitrage in a model of a securities market assuming only that the set of constraints on investment strategies (portfolios) is closed and convex. We use the language of nonstandard analysis to formulate the corresponding version of the first fundamental theorem of asset pricing. We show that two topological versions of the no-arbitrage condition reduces to it by a change of constraints.