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The Central Knot

In: The Medium of Contingency

Author

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  • Elie Ayache

Abstract

Is it a coincidence that the binomial tree and Brownian motion should yield a complete market, respectively in discrete time and continuous time? That the market should be complete or incom-plete seems to us so dramatic an alternative, yielding alternative consequences so incommensurate with each other,1 that it cannot depend on picking Brownian motion or the binomial tree among a choice of several available stochastic processes, as if another choice were possible and it was only a coincidence that we had picked Brownian motion or the binomial tree. Brownian motion and the binomial tree seem to us to belong to a category of their own inside which it would no longer be a coincidence if we picked them because they fill it completely — their own special category.

Suggested Citation

  • Elie Ayache, 2015. "The Central Knot," Palgrave Macmillan Books, in: The Medium of Contingency, chapter 13, pages 283-299, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-137-28656-7_14
    DOI: 10.1007/978-1-137-28656-7_14
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