Infinitely many securities and the fundamental theorem of asset pricing
AbstractSeveral authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía de la Empresa in its series Business Economics Working Papers with number wb043513.
Date of creation: Aug 2004
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