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On the probability of completeness for large markets

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Abstract

We consider a family of discrete multiperiod multinomial market models F n , each of which contains n − 1 stocks and one bond. All the securities are allowed to be risky and we assume that the number of states in each period is finite. We let the securities’ prices follow probability distributions that reflect the traders’ view of the market. Under mild restrictions on the probability structure of F n , we show that the probability that a market, chosen at random from F n , is complete tends to one as n approaches infinity.

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Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Hong Kong, Hong Kong, China

    John A. Wright

  2. Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China

    Phillip S. C. Yam

  3. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China

    Hailiang Yang

Authors
  1. John A. Wright
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  2. Phillip S. C. Yam
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  3. Hailiang Yang
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Corresponding author

Correspondence to Hailiang Yang.

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Wright, J.A., Yam, P.S.C. & Yang, H. On the probability of completeness for large markets. Japan J. Indust. Appl. Math. 28, 301–313 (2011). https://doi.org/10.1007/s13160-011-0040-2

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  • DOI: https://doi.org/10.1007/s13160-011-0040-2

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