Large volatility-stabilized markets

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• 作者：Mykhaylo Shkolnikov ^{mshkolni@math.stanford.edu mshkolni@gmail.com}
• 关键词：60J60 ; 60J70 ; 91G80
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：January, 2013
• 年：2013
• 卷：123
• 期：1
• 页码：212-228
• 全文大小：302 K

文摘

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.