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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)

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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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Paper provided by HAL in its series Post-Print with number halshs-00167157_v1.

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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_v1

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ross, Stephen A, 1987. "Arbitrage and Martingales with Taxation," Journal of Political Economy, University of Chicago Press, vol. 95(2), pages 371-93, April. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Dybvig, Philip H & Ross, Stephen A, 1986. " Tax Clienteles and Asset Pricing," Journal of Finance, American Finance Association, vol. 41(3), pages 751-62, July. [Downloadable!] (restricted)
  4. 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 99-036, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  5. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
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  6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  8. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October. [Downloadable!] (restricted)
  9. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August. [Downloadable!] (restricted)
  10. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478. [Downloadable!] (restricted)
  11. Grossman, Sanford J & Laroque, Guy, 1990. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," Econometrica, Econometric Society, vol. 58(1), pages 25-51, January. [Downloadable!] (restricted)
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  12. Prisman, Eliezer Z, 1986. " Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, vol. 41(3), pages 545-57, July. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Chambers, Robert G. & Quiggin, John, 2002. "Resource Allocation And Asset Pricing," Working Papers 28571, University of Maryland, Department of Agricultural and Resource Economics. [Downloadable!]
    Other versions:
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