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. 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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Bibliographic InfoPaper provided by Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/12972.
Length: 343 p.
Date of creation: Oct 2007
Date of revision:
Publication status: Published in Mediterranean Journal of Mathematics (2007-10) v.v. 4, p.321-341
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Web page: http://www.uc3m.es
Infinitely many securities; Arbitrage; Martingale measure; Projective system;
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- Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
- J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
- Elyès Jouini & Hédi Kallal, 1999.
"Efficient Trading Strategies in the Presence of Market Frictions,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-035, New York University, Leonard N. Stern School of Business-.
- Jouini, Elyes & Kallal, Hedi, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 343-69.
- Elyès Jouini & Hédi Kallal, 1998. "Efficient Trading Strategies in the Presence of Market Frictions," Working Papers 98-31, Centre de Recherche en Economie et Statistique.
- Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
- Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2007. "Risk-neutral valuation with infinitely many trading dates," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/13981, Universidad Carlos III de Madrid.
- Aliprantis, C. D. & Florenzano, M. & Martins-da-Rocha, V. F. & Tourky, R., 2004.
"Equilibrium analysis in financial markets with countably many securities,"
Journal of Mathematical Economics,
Elsevier, vol. 40(6), pages 683-699, September.
- Charalambos Aliprantis & Monique Florenzano & Victor-Filipe Martins-Da-Rocha & Rabee Tourky, 2004. "Equilibrium analysis in financial markets with countably many securities," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00086810, HAL.
- repec:fth:inseep:9513 is not listed on IDEAS
- Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
- Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
- Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
- Balbas, Alejandro & Miras, Miguel Angel & Munoz-Bouzo, Maria Jose, 2002. "Projective system approach to the martingale characterization of the absence of arbitrage," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 311-323, July.
- (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
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