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An Elementary Exposition of the No Strong Arbitrage Principle for Financial Markets

Author

Listed:
  • Robert A. Becker

    (Indiana University)

Abstract

A Linear Pricing Rule is established for the No Strong Arbitrate Principle (NSAP) in a finite state, single period asset pricing model. The (NSAP) condition is a statement about the inconsistency of a particular system of linear inequalities. The novelty here lies in the use of the Kuhn-Motzkin-Fourier elimination technique that derives the corresponding dual linear inequality system using elementary methods only. The advantage is that a familiar computational scheme yields the relationship between the (NSAP) inequalities and their dual system. Indeed, the method uncovers why the dual inequality system is, in fact, a dual system in the first place. Students and researchers unfamiliar with systems of dual linear inequalities and Theorems of the Alternative may find the approach taken here as a way to better understand the motivation and use of these techniques.

Suggested Citation

  • Robert A. Becker, 2017. "An Elementary Exposition of the No Strong Arbitrage Principle for Financial Markets," CAEPR Working Papers 2017-005, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2017005
    as

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    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2017-005.pdf
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    References listed on IDEAS

    as
    1. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1.
    2. Bailey,Roy E., 2005. "The Economics of Financial Markets," Cambridge Books, Cambridge University Press, number 9780521612807, September.
    3. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2.
    4. Varian, Hal R, 1987. "The Arbitrage Principle in Financial Economics," Journal of Economic Perspectives, American Economic Association, vol. 1(2), pages 55-72, Fall.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    No Strong Arbitrage; arbitrage; Farkas Lemma; Kuhn-Motzkin-Fourier Elimination; state prices; linear inequalities;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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