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Finitely Additive Equivalent Martingale Measures

Author

Listed:
  • 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)

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

Suggested Citation

  • Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Finitely Additive Equivalent Martingale Measures," Quaderni di Dipartimento 123, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:123
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    References listed on IDEAS

    as
    1. Patrizia Berti & Eugenio Regazzini & Pietro Rigo, 2001. "Strong previsions of random elements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 11-28, January.
    2. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
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