Università della Svizzera italiana

Supermartingale decomposition with a general index set

Cassese, Gianluca

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.

Università della Svizzera italiana

Quasimartingales with a linearly ordered index set

Cassese, Gianluca ; della Svizzera italiana, Svizzera

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.

Università della Svizzera italiana

Finitely additive supermartingales

Cassese, Gianluca

In: Journal of theoretical probability, 2008, vol. 21, no. 3, p. 586-603

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 Doléans-Dade 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...

Università della Svizzera italiana

A note on asset bubbles in continuous-time

Cassese, Gianluca

In: International journal of theoretical and applied finance, 2005, vol. 8, no. 4, p. 523-536

In this paper we propose a model of asset prices consistent with the no-arbitrage 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.

Università della Svizzera italiana

Sure wins, separating probabilities and the representation of linear functionals

Cassese, Gianluca

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...

Università della Svizzera italiana

Modelling the implied volatility surface : Does market efficiency matter? : an application to MIB30 index options

Cassese, Gianluca ; Guidolin, Massimo

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...

Università della Svizzera italiana

Pricing and informational efficiency of the MIB30 index options market : an analysis with high-frequency data

Cassese, Gianluca ; Guidolin, Massimo

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...

Università della Svizzera italiana

Decomposition of supermartingales indexed by a linearly

Cassese, Gianluca

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.

Università della Svizzera italiana

Yan theorem in L ∞ with applications to asset pricing

Cassese, Gianluca

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.

Università della Svizzera italiana

Asset pricing with no exogenous probability measure

Cassese, Gianluca

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,...