On the probability of completeness for large markets

John A. Wright; Phillip S.C. Yam; Hailiang Yang

doi:10.1007/s13160-011-0040-2

On the probability of completeness for large markets

John A. Wright, Phillip S.C. Yam, Hailiang Yang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	301-313
Number of pages	13
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s13160-011-0040-2
Publication status	Published - Aug 2011
Externally published	Yes

Keywords

General linear groups over a finite field
Largemarkets
Market completeness
Multiperiod model
Single periodmodel

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KW - Largemarkets

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KW - Multiperiod model

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On the probability of completeness for large markets

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Keywords

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