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Market free lunch and large financial markets

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  • Irene Klein

Abstract

The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage are characterized in terms of no asymptotic market free lunch; the difference lies in the set of utilities. In particular, it is shown directly that no asymptotic market free lunch with respect to monotone concave utilities is equivalent to no asymptotic free lunch. In principle, the paper can be seen as the large financial market analogue of [Math. Finance 14 (2004) 351--357] and [Math. Finance 16 (2006) 583--588].

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  • Irene Klein, 2007. "Market free lunch and large financial markets," Papers math/0702409, arXiv.org.
    • Handle: RePEc:arx:papers:math/0702409
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    References listed on IDEAS

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    1. Irene Klein, 2006. "A Comment On Market Free Lunch And Free Lunch," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 583-588, July.
    2. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    3. Sen, P. K. & Tsong, Y., 1980. "On functional central limit theorems for certain continuous time parameter stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 371-378, September.
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