An extended version of the Dalang–Morton–Willinger theorem under portfolio constraints

This work considers an extension of the Dalang–Morton–Willinger theorem (the first fundamental theorem of asset pricing) in the presence of random convex constraints on the asset portfolio. The arbitrage-free assumption is characterized both in terms of a natural generalization of the notion of the martingale measure and in terms of supports of conditional distributions of price increments. The proposed approach relies on the well-known results for the case of a perfect market and is connected with the theory of measurable set-valued mappings.