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Continuous Time Processes with Stable Increments

J. Huston McCulloch
The Journal of Business
Vol. 51, No. 4 (Oct., 1978), pp. 601-619
Stable URL: http://www.jstor.org/stable/2352652
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Continuous Time Processes with Stable Increments
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Abstract

It is well known that the continuous time sample paths of variables with stable increments contain infinitely many discontinuities. This paper derives the distribution of the largest discontinuity in the intermediate stable case and of all the discontinuities in the "worst" Cauchy case. The discontinuities prove not unmanageable and even economically attractive. The greater "cohesion" of stable processes actually makes arbitrage easier than with a diffusion process. Furthermore, the infinite expected returns with log-stable price changes are theoretically compatible with finite asset prices. We conclude that the stable assumption should be given serious attention in financial model building.

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