In: Journal of Theoretical Probability, 2008, vol. 21, no. 3, p. 586603

In: Stochastic processes and their applications, 2010, vol. 120, no. 7, p. 10601073
We prove results on the existence of DoléansDade measures and of the DoobMeyer decomposition for supermartingales indexed by a general index set.

In: Statistics & probability letters, 2010, vol. 80, no. 56, p. 421426
We consider quasimartingales 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.

In: Journal of theoretical probability, 2008, vol. 21, no. 3, p. 586603
The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated DoléansDade measure. We obtain versions of the Doob–Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no...

In: International journal of theoretical and applied finance, 2005, vol. 8, no. 4, p. 523536
In this paper we propose a model of asset prices consistent with the noarbitrage principle but allowing for the existence of "bubbles". The structure of bubbles is explicitly characterized and we show that, for example, they may be of either sign. Furthermore, we discuss the existence of bubbles under alternative definitions of absence of arbitrage opportunities.

In: Journal of mathematical analysis and applications, 2009, vol. 354, no. 2, p. 558563
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...

In: International review of financial analysis, 2006, vol. 15, no. 2, p. 145178
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, BlackScholes benchmark. This result is robust to alternative...

In: Economic notes, 2004, vol. 33, no. 2, p. 275321
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 noarbitrage conditions. This percentage declines when we relax the noarbitrage restrictions to accommodate for the presence of bid/ask spreads and other...

In: Statistics & probability letters, 2007, vol. 77, no. 8, p. 795802
We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set.

In: Acta mathematicae applicatae sinica, 2007, vol. 23, no. 4, p. 551562
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.
