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Efficiency analysis, shortage functions, arbitrage, and martingales

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  • Chambers, Robert G.
  • Färe, Rolf

Abstract

This paper shows that standard tools of efficiency analysis, directional distance functions, can be used to characterize the investment-returns technology. That ability to characterize the investment-returns technology and fundamental duality relationships imply that directional distance functions can be used to detect the presence of an arbitrage, to value financial assets in the absence of an arbitrage lying in the span of the market and to place bounds on the no-arbitrage values of assets lying outside the span of the market.

Suggested Citation

  • Chambers, Robert G. & Färe, Rolf, 2011. "Efficiency analysis, shortage functions, arbitrage, and martingales," European Journal of Operational Research, Elsevier, vol. 213(1), pages 349-358, August.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:1:p:349-358
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    References listed on IDEAS

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    1. W. Briec & K. Kerstens & J. B. Lesourd, 2004. "Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 1-27, January.
    2. Chambers, Robert G. & Quiggin, John, 2008. "Narrowing the no-arbitrage bounds," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 1-14, January.
    3. Timo Kuosmanen, 2007. "Performance measurement and best-practice benchmarking of mutual funds: combining stochastic dominance criteria with data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 28(1), pages 71-86, October.
    4. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    5. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    6. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    8. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    9. Prisman, Eliezer Z, 1986. "Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, vol. 41(3), pages 545-557, July.
    10. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    11. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
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