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Market viability via absence of arbitrage of the first kind

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Abstract

It is shown that, in a semimartingale financial market model, there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.

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References

  1. Bichteler, K.: Stochastic Integration with Jumps. Encyclopedia of Mathematics and Its Applications, vol. 89. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  2. Brannath, W., Schachermayer, W.: A bipolar theorem for \(L^{0}_{+}(\varOmega , \mathcal{F}, \mathbf{P})\). In: Séminaire de Probabilités, XXXIII. Lecture Notes in Math., vol. 1709, pp. 349–354. Springer, Berlin (1999)

    Chapter  Google Scholar 

  3. Dalang, R.C., Morton, A., Willinger, W.: Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stoch. Stoch. Rep. 29, 185–201 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Delbaen, F., Schachermayer, W.: A general version of the fundamental theorem of asset pricing. Math. Ann. 300, 463–520 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Delbaen, F., Schachermayer, W.: The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312, 215–250 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fernholz, E., Karatzas, I.: Stochastic portfolio theory: an overview. In: Bensoussan, A. (ed.) Handbook of Numerical Analysis. Mathematical Modeling and Numerical Methods in Finances, pp. 89–168 (2009)

    Google Scholar 

  7. Föllmer, H., Kabanov, Y.M.: Optional decomposition and Lagrange multipliers. Finance Stoch. 2, 69–81 (1998)

    MathSciNet  MATH  Google Scholar 

  8. Gilles, C., LeRoy, S.F.: Bubbles and charges. Int. Econ. Rev. 33, 323–339 (1992)

    Article  MATH  Google Scholar 

  9. Harrison, J.M., Kreps, D.M.: Martingales and arbitrage in multiperiod securities markets. J. Econ. Theory 20, 381–408 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ingersoll, J.E.: Theory of Financial Decision Making. Rowman & Littlefield Studies in Financial Mathematics. Rowman & Littlefield, Totowa (1987)

    Google Scholar 

  11. Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes, 2nd edn., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 288. Springer, Berlin (2003)

    MATH  Google Scholar 

  12. Kabanov, Y.M.: On the FTAP of Kreps–Delbaen–Schachermayer. In: Kabanov, Y.M., Rozovskii, B.L., Shiryaev, A.N. (eds.) Statistics and Control of Stochastic Processes, Moscow, 1995/1996, pp. 191–203. World Sci. Publ., River Edge (1997)

    Google Scholar 

  13. Kabanov, Y.M., Kramkov, D.O.: Large financial markets: asymptotic arbitrage and contiguity. Teor. Veroâtn. Ee Primen. 39, 222–229 (1994)

    MathSciNet  MATH  Google Scholar 

  14. Kabanov, Y.M., Liptser, R.S., Shiryaev, A.N.: Absolute continuity and singularity of locally absolutely continuous probability distributions. (I). Mat. Sb. 107, 364–415 (1978)

    MathSciNet  Google Scholar 

  15. Kallsen, J.: σ-localization and σ-martingales. Teor. Veroâtn. Ee Primen. 48, 177–188 (2003)

    MathSciNet  Google Scholar 

  16. Karatzas, I., Kardaras, C.: The numéraire portfolio in semimartingale financial models. Finance Stoch. 11, 447–493 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kardaras, C.: Finitely additive probabilities and the fundamental theorem of asset pricing. In: Chiarella, C., Novikov, A. (eds.) Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, pp. 19–34. Springer, Berlin (2010)

    Google Scholar 

  18. Loewenstein, M., Willard, G.A.: Local martingales, arbitrage, and viability. Free snacks and cheap thrills. Econom. Theory 16, 135–161 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Loewenstein, M., Willard, G.A.: Rational equilibrium asset-pricing bubbles in continuous trading models. J. Econ. Theory 91, 17–58 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Platen, E., Heath, D.: A Benchmark Approach to Quantitative Finance. Springer Finance. Springer, Berlin, (2006)

    Book  MATH  Google Scholar 

  21. Rogers, L.C.G.: Equivalent martingale measures and no-arbitrage. Stoch. Stoch. Rep. 51, 41–49 (1994)

    MATH  Google Scholar 

  22. Rokhlin, D.B.: Asymptotic arbitrage and numéraire portfolios in large financial markets. Finance Stoch. 12, 173–194 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Schweizer, M.: On the minimal martingale measure and the Föllmer–Schweizer decomposition. Stoch. Anal. Appl. 13, 573–599 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank Yuri Kabanov for fruitful conversations that significantly helped in formulating and proving the results of this paper. Two anonymous referees provided invaluable help in the presentation of the paper.

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  1. Mathematics and Statistics Department, Boston University, 111 Cummington Street, Boston, MA, 02215, USA

    Constantinos Kardaras

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  1. Constantinos Kardaras
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Correspondence to Constantinos Kardaras.

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Kardaras, C. Market viability via absence of arbitrage of the first kind. Finance Stoch 16, 651–667 (2012). https://doi.org/10.1007/s00780-012-0172-5

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  • DOI: https://doi.org/10.1007/s00780-012-0172-5

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