The Annals of Applied Probability

Dynamics of observables in rank-based models and performance of functionally generated portfolios

Sergio A. Almada Monter, Mykhaylo Shkolnikov, and Jiacheng Zhang

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In the seminal work (Stochastic Portfolio Theory: Stochastic Modelling and Applied Probability (2002) Springer), several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. We fill this gap in the setting of rank-based models. The results are then used to study the performance of multiplicatively and additively functionally generated portfolios.

Article information

Ann. Appl. Probab., Volume 29, Number 5 (2019), 2849-2883.

Received: February 2018
Revised: November 2018
First available in Project Euclid: 18 October 2019

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Mathematical Reviews number (MathSciNet)

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 91G10: Portfolio theory
Secondary: 60G15: Gaussian processes 60H15: Stochastic partial differential equations [See also 35R60]

Capital distribution functionally generated portfolios Gaussian fluctuations hitting times hydrodynamic limits macroscopic market observables market diversity market entropy porous medium equation rank-based models relative return stochastic partial differential equations stochastic portfolio theory


Almada Monter, Sergio A.; Shkolnikov, Mykhaylo; Zhang, Jiacheng. Dynamics of observables in rank-based models and performance of functionally generated portfolios. Ann. Appl. Probab. 29 (2019), no. 5, 2849--2883. doi:10.1214/19-AAP1466.

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