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Arbitrage and Growth Rate for Riskless Investments in a Stationary Economy

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  • Ilan Adler
  • David Gale

Abstract

A sequential investment is a vector of payments over time, (a0, a1, ... ,an), where a payment is made to or by the investor according as ai is positive or negative. Given a collection of such investments it may be possible to assemble a portfolio from which an investor can get “something for nothing,” meaning that without investing any money of his own he can receive a positive return after some finite number of time periods. Cantor and Lipmann (1995) have given a simple necessary and sufficient condition for a set of investments to have this property. We present a short proof of this result. If arbitrage is not possible, our result leads to a simple derivation of the expression for the long–run growth rate of the set of investments in terms of its “internal rate of return.”

Suggested Citation

  • Ilan Adler & David Gale, 1997. "Arbitrage and Growth Rate for Riskless Investments in a Stationary Economy," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 73-81, January.
    • Handle: RePEc:bla:mathfi:v:7:y:1997:i:1:p:73-81
    DOI: 10.1111/1467-9965.00023
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    Cited by:

    1. Carassus, Laurence & Jouini, Elyes, 2000. "A discrete stochastic model for investment with an application to the transaction costs case," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 57-80, February.
    2. Igor Evstigneev & Dhruv Kapoor, 2009. "Arbitrage in stationary markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 5-12, May.
    3. 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.

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