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Market imperfections, equilibrium and arbitrage

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  • Elyès Jouini

Abstract

The theory of asset pricing, which takes its roots in the Arrow-Debreu model (Theory of value [1959, chap. 7]), the Black and Sholes formula (1973) and Cox and Ross (1976 a and b), has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1979) and Kreps (1981). In these models, securities markets are assumed to be frictionless. The main result is that a price process is arbitrage free (or, equivalently, compatible with some equilibrium) if and only if it is, when appropriately renormalized, a martingale for some equivalent probability measure. The theory of pricing by arbitrage follows from there. Contingent claims can be priced by taking their expected value with respect to an equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage. The new probabilities can be interpreted as state prices (the prices of $1$ dollar tomorrow in each state of the world) or as the intertemporal marginal rates of substitution of an agent maximizing his expected utility. In this work, we will propose a general model that takes frictions into account.

Suggested Citation

  • Elyès Jouini, 2003. "Market imperfections, equilibrium and arbitrage," Finance 0312005, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0312005
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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Philip H. Dybvig, Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 377-401.
    3. Aiyagari, S. Rao & Gertler, Mark, 1991. "Asset returns with transactions costs and uninsured individual risk," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 311-331, June.
    4. Dybvig, Philip H & Ross, Stephen A, 1986. "Tax Clienteles and Asset Pricing," Journal of Finance, American Finance Association, vol. 41(3), pages 751-762, July.
    5. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    6. Cantor, David G & Lippman, Steven A, 1995. "Optimal Investment Selection with a Multitude of Projects," Econometrica, Econometric Society, vol. 63(5), pages 1231-1240, September.
    7. Dybvig, Philip H & Ross, Stephen A, 1985. "The Analytics of Performance Measurement Using a Security Market Line," Journal of Finance, American Finance Association, vol. 40(2), pages 401-416, June.
    8. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    9. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    12. Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1991. "Cash Stream Valuation In the Face of Transaction Costs and Taxes," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 31-54, January.
    13. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    14. John H. Cochrane & Lars Peter Hansen, 1992. "Asset Pricing Explorations for Macroeconomics," NBER Chapters, in: NBER Macroeconomics Annual 1992, Volume 7, pages 115-182, National Bureau of Economic Research, Inc.
    15. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-251, April.
    16. repec:arz:wpaper:eres1993-121 is not listed on IDEAS
    17. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
    18. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    19. Aiyagari, S. Rao & Gertler, Mark, 1991. "Asset returns with transactions costs and uninsured individual risk," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 311-331, June.
    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, vol. 14(1), pages 35-51, February.
    21. Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-1546, November.
    22. 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.
    23. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    24. 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 637-654, May-June.
    25. Laurence Carassus & Elyès Jouini, 1998. "Investment and Arbitrage Opportunities with Short Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 169-178, July.
    26. Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1995. "Tax Basis And Nonlinearity In Cash Stream Valuation," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 97-119, April.
    27. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    28. Cantor, David G & Lippman, Steven A, 1983. "Investment Selection with Imperfect Capital Markets," Econometrica, Econometric Society, vol. 51(4), pages 1121-1144, July.
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    Cited by:

    1. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    2. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    3. Dokuchaev, N. G. & Savkin, Andrey V., 2004. "Universal strategies for diffusion markets and possibility of asymptotic arbitrage," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 409-419, June.
    4. Nikolai Dokuchaev, 2002. "Pricing rule based on non-arbitrage arguments for random volatility and volatility smile," Papers math/0205120, arXiv.org.

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    More about this item

    Keywords

    transaction costs; shortsales constraints; frictions; market imperfections; arbitrage; viability; different borrowing and lending rates; borrowing constraints; arbitrage pricing;
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    JEL classification:

    • G - Financial Economics

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