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On the probability of completeness for large markets

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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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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Keywords

  • Market completeness
  • Large markets
  • Single period model
  • Multiperiod model
  • General linear groups over a finite field

Mathematics Subject Classification (2000)

  • 91G99
  • 60B20