大波动稳定市场
Large volatility-stabilized markets
摘要：
我们研究了相互作用的扩散过程系统的行为，在数学金融文献中称为波动稳定的市场模型，当扩散的数量趋于无穷大。我们表明，经过适当的时间参数的重新缩放，系统的经验措施收敛到退化抛物型偏微分方程的解决方案。一个随机表示后者的一维分布的时变平方贝塞尔过程允许我们给出一个明确的描述的限制。
英文摘要：
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an appropriate rescaling of the time parameter, the empirical measure of the system converges to the solution of a degenerate parabolic partial differential equation. A stochastic representation of the latter in terms of one-dimensional distributions of a time-changed squared Bessel process allows us to give an explicit description of the limit.
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