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Arbitrage and viability in securities markets with fixed trading costs

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Author Info

  • Elyès Jouini

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

  • Hedi Kallal

    (SBS - salomon barney smith - Smith Barney Investments)

  • Clotilde Napp

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

Abstract

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.

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File URL: http://halshs.archives-ouvertes.fr/docs/00/16/71/57/PDF/27-CF3008_Kallal_Napp_Arbitrage_and_Viability_in_Securities_Markets_with_Fixed_Tradind_Costs.pdf
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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00167157.

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Date of creation: 2001
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Publication status: Published, Journal of Mathematical Economics, 2001, 197-221
Handle: RePEc:hal:journl:halshs-00167157

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00167157/en/
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Related research

Keywords: Arbitrage; Fixed costs; Absolutely continuous Martingale measure; Contingent claims pricing;

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References

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  1. Sanford J. Grossman & Guy Laroque, 1987. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," NBER Working Papers 2369, National Bureau of Economic Research, Inc.
  2. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 66(1), pages 178-197, June.
  3. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(2), pages 133-165.
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  5. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(4), pages 337-356.
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  8. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers, University of California at Berkeley RPF-191, University of California at Berkeley.
  9. Jouini, Elyès & Kallal, Hedi, 1999. "Viability and equilibrium in securities markets with frictions," Economics Papers from University Paris Dauphine 123456789/5603, Paris Dauphine University.
  10. Dybvig, Philip H & Ross, Stephen A, 1986. " Tax Clienteles and Asset Pricing," Journal of Finance, American Finance Association, American Finance Association, vol. 41(3), pages 751-62, July.
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  12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  13. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(4), pages 842-62, August.
  14. Prisman, Eliezer Z, 1986. " Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, American Finance Association, vol. 41(3), pages 545-57, July.
  15. 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.
  16. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-036, New York University, Leonard N. Stern School of Business-.
  17. 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.
  18. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
  19. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
  20. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 14(1), pages 35-51, February.
  21. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(2), pages 245-263, October.
  22. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(3), pages 197-232.
  23. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 11(3), pages 215-260, August.
  24. Hindy, Ayman, 1995. "Viable prices in financial markets with solvency constraints," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 105-135.
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  26. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
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Citations

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Cited by:
  1. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
  2. Chambers, Robert G. & Quiggin, John C., 2002. "Resource Allocation And Asset Pricing," Working Papers, University of Maryland, Department of Agricultural and Resource Economics 28571, University of Maryland, Department of Agricultural and Resource Economics.
  3. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print, HAL halshs-00703138, HAL.

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