Open Access
October 2019 Dynamics of observables in rank-based models and performance of functionally generated portfolios
Sergio A. Almada Monter, Mykhaylo Shkolnikov, Jiacheng Zhang
Ann. Appl. Probab. 29(5): 2849-2883 (October 2019). DOI: 10.1214/19-AAP1466


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.


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Sergio A. Almada Monter. Mykhaylo Shkolnikov. Jiacheng Zhang. "Dynamics of observables in rank-based models and performance of functionally generated portfolios." Ann. Appl. Probab. 29 (5) 2849 - 2883, October 2019.


Received: 1 February 2018; Revised: 1 November 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155061
MathSciNet: MR4019877
Digital Object Identifier: 10.1214/19-AAP1466

Primary: 60H10 , 91G10
Secondary: 60G15 , 60H15

Keywords: 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

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 5 • October 2019
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