The dalang-morton-willinger theorem under delayed and restricted information

Abstract

We extend the classical no-arbitrage criteria to the case of a model where the investor's decisions are based on a partial information (e.g., because of delay or round-off errors), that is the portfolio strategies are predictable with respect to a subfiltration. Our main result is a ramification of the famous Dalang-Morton-Willinger theorem: the model is arbitrage-free if and only if there exists an equivalent probability measure P̃ such that the optional projection of the price process with respect to P̃ is a P̃-martingale.