Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/95312
Authors: 
Berti, Patrizia
Pratelli, Luca
Rigo, Pietro
Year of Publication: 
2010
Series/Report no.: 
Quaderni di Dipartimento 123
Abstract: 
Let L be a linear space of real bounded random variables on the probability space (omega,A, P0). There is a finitely additive probability P on A, such that P tilde P0 and EP (X) = 0 for all X in L, if and only if cEQ(X) = ess sup(-X), X in L, for some constant c > 0 and (countably additive) probability Q on A such that Q tilde P0. A necessary condition for such a P to exist is L - L+(inf) n L+(inf) = {0}, where the closure is in the norm-topology. If P0 is atomic, the condition is sufficient as well. In addition, there is a finitely additive probability P on A, such that P << P0 and EP (X) = 0 for all X in L, if and only if ess sup(X) = 0 for all X in L.
Subjects: 
Arbitrage
de Finetti’s coherence principle
equivalent martingale measure
finitely additive probability
fundamental theorem of asset pricing
Document Type: 
Working Paper

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