An Extended Version of the Dalang--Morton--Willinger Theorem under Portfolio Constraints

Abstract

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.

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