arXiv subjects
Publications and source records attributed to Gianluca Cassese.
We prove some results concerning the finitely additive, vector integral of Bochner and Pettis and their representation over a countably additive probability space. Applications to convergence of vector valued martingales and to the non compact Choquet theorem are provided.
We obtain an elementary characterization of expected utility based on a representation of choice in terms of psychological gambles, which requires no assumption other than coherence between ex-ante and ex-post preferences. Weaker version of coherence are associated with various attitudes towards complexity and lead to a characterization of minimax or Choquet expected utility.
We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several applications to set functions, vector lattices and other more explicit structures are provided.
We prove an easy version of the minimax theorem with no topological assumption. We deduce from it some domination criteria as well as an application to $p$-summing operators.
We investigate the possibility of completing financial markets in a model with no exogenous probability measure and market imperfections. A necessary and sufficient condition is obtained for such extension to be possible.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We provide conditions under which a modular function defined on a semilattice $X$ and with values in a commutative group is homomorphic to a modular function on a lattice $L$ for any embedding $X\hookrightarrow L$.
In this paper we discuss the existence of a control measure for a family of measures on a Boolean algebra. We obtain a necessary and sufficient condition and several related results, including a new criterion for weak compactness for additive set functions on an algebra of sets.
We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study finitely additive conditional probability. We show that this property has many interesting applications in probability as well as in analysis.
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation from which it is possible, as in the original work of Breeden and Litzenberger, to extract the implied probability. Eventually we test this conclusion empirically via a new non parametric approach.
We provide a version of the celebrated theorem of Komlós in which, rather then random quantities, a sequence of finitely additive measures is considered. We obtain a form of the subsequence principle and some applications.
We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we first test the methodology on a simulated sample of option prices and then on the S\&P 500 index options.
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. Eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation which allows, as in Breeden and Litzenberger, to extract the implied probability.
Based on a generalization of Lebesgue decomposition we obtain a characterization of weak compactness in the space $ba$, a representation of its dual space and some results on the structure of finitely additive measures.
Given a generalization of Lebesgue decomposition we obtain an extension to the finitely additive setting of the theorems of Halmos and Savage and of Yan.
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
We prove a version of Rao decomposition for quasi-martingales indexed by a linearly ordered set.