Large volatility-stabilized markets

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Shkolnikov, Mykhaylo

关键词: Interacting diffusion processes;    Hydrodynamic limit;    Volatility-stabilized models;    Bessel processes;    Degenerate parabolic partial differential equations;   

DOI  :  10.1016/j.spa.2012.09.001

来源: Elsevier

【 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 resealing 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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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