Journal
ANNALS OF APPLIED PROBABILITY
Volume 21, Issue 3, Pages 1180-1213Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/10-AAP725
Keywords
Volatility-stabilized markets; Bessel processes; Wright-Fisher model; Kelvin transform; market weights
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Funding
- NSF [DMS-10-07563]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1007563] Funding Source: National Science Foundation
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We derive the joint density of market weights, at fixed times and suitable stopping times, of the volatility-stabilized market models introduced by Fernholz and Karatzas in [Ann. Finan. 1 (2005) 149-177]. The argument rests on computing the exit density of a collection of independent Bessel-square processes of possibly different dimensions from the unit simplex. We show that the law of the market weights is the same as that of the multi-allele Wright-Fisher diffusion model, well known in population genetics. Thus, as a side result, we furnish a novel proof of the transition density function of the Wright-Fisher model which was originally derived by Griffiths by biorthogonal series expansion.
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