In: Stochastic processes and their applications, 2010, vol. 120, no. 7, p. 1060-1073
We prove results on the existence of Doléans-Dade measures and of the Doob-Meyer decomposition for supermartingales indexed by a general index set.
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In: Statistics & probability letters, 2010, vol. 80, no. 5-6, p. 421-426
We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.
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In: Journal of mathematical analysis and applications, 2009, vol. 354, no. 2, p. 558-563
We discuss conditions under which a convex cone K ⊂ RΩ admits a finitely additive probability m such that supk∈K m(k) ≤ 0. Based on these, we characterize those linear functionals that are representable as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable...
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In: International review of financial analysis, 2006, vol. 15, no. 2, p. 145-178
We analyze the volatility surface vs. moneyness and time to expiration implied by MIBO options written on the MIB30, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark. This result is robust to alternative...
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In: Economic notes, 2004, vol. 33, no. 2, p. 275-321
We analyze the pricing and informational efficiency of the Italian market for options written on the most important stock index, the MIB30. We report that a striking percentage of the data consists of option prices violating basic no-arbitrage conditions. This percentage declines when we relax the no-arbitrage restrictions to accommodate for the presence of bid/ask spreads and other...
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In: Statistics & probability letters, 2007, vol. 77, no. 8, p. 795-802
We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set.
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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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We analyze the pricing and informational effciency of the Italian market for options written on the most important stock index, the MIB30. We find several indications inconsistent with the hypothesis that the Italian MIBO is an effcient market. We report that a striking percentage of the data consists of option prices violating basic no-arbitrage conditions. This percentage declines but never...
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