ANALYSIS OF MARKET WEIGHTS UNDER VOLATILITY-STABILIZED MARKET MODELS

作者：Pal Soumik^*

来源：Annals of Applied Probability, 2011, 21(3): 1180-1213.

DOI：10.1214/10-AAP725

• Volatility-stabilized markets
• Bessel processes
• Wright-Fisher model
• Kelvin transform
• market weights

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.

• 出版日期2011-6