Arbitrage and Growth Rate for Riskless Investments in a Stationary Economy |
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Authors: | Ilan Adler & David Gale |
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Institution: | IEOR Department, University of California, Berkeley, CA,;Mathematics Department, University of California, Berkeley, CA |
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Abstract: | A sequential investment is a vector of payments over time, ( a 0, a 1, ... , 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." |
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Keywords: | investment program growth rate no arbitrage cash stream valuation positive polynomial convolution of vectors |
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