In: Acta Mathematicae Applicatae Sinica, English Series, 2007, vol. 23, no. 4, p. 551-562
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In: Acta mathematicae applicatae sinica, 2007, vol. 23, no. 4, p. 551-562
We prove an L∞ version of Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets in which asset prices are a continuous Rd valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.
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In: Mathematical finance, 2008, vol. 18, no. 1, p. 23-54
In this paper we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure,...
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Finitely additive martingales are the counterpart of finitely additive measures over filtered probability space. We study the structure of the Yosida Hewitt decomposition in such setting and obtaing a full characterisation. Based on this result we introduce a “conditional expectation” operator for finitely additive measures which has some properties in common with ordinary conditional...
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