Fundamental Theorem of Asset Pricing under Transaction costs and Model\n uncertainty

2013/09/05 by Erhan Bayraktar, Bayraktar, Erhan, Yuchong Zhang +1 · 1 citation
Economics, Econometrics and Finance · #60G42 #91B28 #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1309.1420

openalex publication_date 2013/09/05 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

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