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On the Order Form of the Fundamental Theorems of Asset Pricing

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DOI: 10.4236/jmf.2014.44019    2,674 Downloads   3,138 Views   Citations

ABSTRACT

In this article, we provide an order-form of the First and the Second Fundamental Theorem of Asset Pricing both in the one-period market model for a finite and infinite state-space and in the case of multi-period model for a finite state-space and a finite time-horizon. The space of the financial positions is supposed to be a Banach lattice. We also prove relevant results in the case where the space of the financial positions is not ordered by a lattice cone.

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Kountzakis, C. (2014) On the Order Form of the Fundamental Theorems of Asset Pricing. Journal of Mathematical Finance, 4, 221-233. doi: 10.4236/jmf.2014.44019.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Delbaen, F. and Schachermayer, W. (1994) A General Version of the Fundamental Theorem of Asset Pricing. Mathematische Annalen, 300, 463-520.
http://dx.doi.org/10.1007/BF01450498
[2] Delbaen, F. and Schachermayer, W. (1998) The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes. Mathematische Annalen, 312, 215-250.
http://dx.doi.org/10.1007/s002080050220
[3] Kreps, D.M. (1981) Arbitrage and Equilirium in Economies with Infinitely Many Commodities. Journal of Mathematical Economics, 8, 15-35.
http://dx.doi.org/10.1016/0304-4068(81)90010-0
[4] Schachermayer, W. (2002) No Arbitrage: On the Work of David Kreps. Positivity, 6, 359-368.
http://dx.doi.org/10.1023/A:1020262419556
[5] Acciaio, B., Beiglbock, M., Penkner, F. and Schachermayer, W. (2013) A Model-Free Version of the Fundamental Theorem of Asset Pricing and the Super-Replication Theorem. Mathematical Finance (to Appear), 6 December 2013.
http://dx.doi.org/10.1111/mafi.12060
[6] Troitsky, V.G. (2005) Martingales in Banach lattices. Positivity, 9, 437-456.
http://dx.doi.org/10.1007/s11117-004-2769-1
[7] Kountzakis, C. and Polyrakis, I.A. (2006) The Completion of Security Markets. Decisions in Economics and Finance, 29, 1-21.
http://dx.doi.org/10.1007/s10203-006-0059-z
[8] Casini, E., Miglierina, E., Polyrakis, I.A. and Xanthos, F. (2013) Reflexive Cones. Positivity, 17, 911-933.
http://dx.doi.org/10.1007/s11117-012-0212-6
[9] Rokhlin, D.B. (2005) The Kreps-Yan Theorem for . International Journal of Mathematics and Mathematical Sciences, 17, 2749-2756.
[10] Rokhlin, D.B. (2009) The Kreps-Yan Theorem for Ideal Banach Spaces. Siberian Mathematical Journal, 50, 162-166.
[11] Polyrakis, I.A. (1996) Finite-Dimensional Lattice-Subspaces of and Curves of . Transactions of the American Mathematical Society, 348, 2793-2810.
http://dx.doi.org/10.1090/S0002-9947-96-01639-X
[12] Schachermayer, W. (1992) A Hilbert Space Proof of the Fundamental Theorem of Asset Pricing in Finite Discrete Time. Insurance: Mathematics and Economics, 11, 249-257.
http://dx.doi.org/10.1016/0167-6687(92)90013-2
[13] Polyrakis, I.A. (1999) Minimal Lattice Subspaces. Transactions of the American Mathematical Society, 351, 4183-4203.
[14] Polyrakis, I.A. (2003) Linear Optimization in and Portfolio Insurance. Optimization, 52, 221-239.
[15] Magill, M. and Quinzii, M. (1996) Theory of Incomplete Markets. MIT Press, location.
[16] Musiela, M. and Rutkowski, M. (1997) Martingale Methods in Financial Modelling. Applications of Mathematics, Mathematical Modelling and Applied Probability, Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-22132-7
[17] Jameson, G. (1970) Ordered Linear Spaces. Lecture Notes in Mathematics, Springer-Verlag, Berlin.
[18] Megginson, R.E. (1998) An Introduction to Banach Spaces. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-0603-3
[19] Bessaga, C. and Pelczyński, A. (1958) On Bases and Unconditional convergence of Series in Banach Spaces. Studia Mathematica, 17, 151-164.
[20] Aliprantis, C.D. and Border, K.C. (2005) Infinite Dimensional Analysis, A Hitchhiker’s Guide. 3rd Edition, Springer, Berlin.

  
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