Martingale and Arbitrage in securities markets with transaction cost

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Abstract
We derive the implications from the absence of arbitrage in dynamic securities market with bi-ask spreads. The absence of arbitrage is equivalent to the existence of at least an equivalent probability measure that transforms some process between the bid and the ask price processes of traded securities into a martingale. These martingale measures can be interpreted as possible linear pricing rules and can be used to determine the investment opportunities available in such an economy. The minimum cost at which a contingent claim can be obtained through securities trading is its largest expected value with respect to the martingale measures.
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