Finitely Additive Equivalent Martingale Measures

Patrizia Berti, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Department of Mathematics, University of Modena and Reggio Emilia
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 123, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

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

Keywords: Arbitrage; de Finetti’s coherence principle; equivalent martingale measure; finitely additive probability; fundamental theorem of asset pricing. (search for similar items in EconPapers)
Pages: 11 pages
Date: 2010-09
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