Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty

Erhan Bayraktar; Yuchong Zhang

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arXiv · 1309.1420

Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty

Erhan Bayraktar·Yuchong Zhang

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Abstract

We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated. Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies \emph{efficient friction}, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.

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BibTeX RIS

Erhan Bayraktar, Yuchong Zhang. 2015-08-30. Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty. https://arxiv.org/abs/1309.1420

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