Publication: Infinitely many securities and the fundamental theorem of asset pricing
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2007-10
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Springer
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Abstract
Several authors have pointed out the possible absence of martingale
measures for static arbitrage free markets with an infinite number of available
securities. Accordingly, the literature constructs martingale measures by generalizing
the concept of arbitrage (free lunch, free lunch with bounded risk,
etc.) or introducing the theory of large financial markets. This paper does
not modify the definition of arbitrage and addresses the caveat by drawing
on projective systems of probability measures. Thus we analyze those situations
for which one can provide a projective system of σ−additive measures
whose projective limit may be interpreted as a risk-neutral probability of an
arbitrage free market. Hence the Fundamental Theorem of Asset Pricing is
extended so that it can apply for models with infinitely many assets.
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Infinitely many securities, Arbitrage, Martingale measure, Projective system
Bibliographic citation
Mediterranean Journal of Mathematics, 2007, v. 4, nº 3, pp. 321-341