## The Annals of Applied Probability

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

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1571385624

Digital Object Identifier
doi:10.1214/19-AAP1466

Mathematical Reviews number (MathSciNet)
MR4019877

#### Citation

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. https://projecteuclid.org/euclid.aoap/1571385624

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