波动稳定市场模型下的市场权重分析
Analysis of market weights under volatility-stabilized market models
摘要：
我们推导了Fernholz和Karatzas在[Ann. Finan. 1（2005）149-177]。该论点依赖于计算出口密度的一组独立的贝塞尔平方过程可能不同的维度从单位单纯形。我们表明，市场权重的法律是相同的多等位基因赖特-费舍尔扩散模型，众所周知的人口遗传学。因此，作为一个副结果，我们提供了一个新的证明的转移密度函数的赖特-费舍尔模型，最初由格里菲斯通过双正交级数展开。
英文摘要：
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 bi-orthogonal series expansion.
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