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Optimal growth trajectories with finite carrying capacity

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C; (2016) Optimal growth trajectories with finite carrying capacity. Physical Review E , 94 , Article 022315. 10.1103/PhysRevE.94.022315. Green open access

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Abstract

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Type: Article
Title: Optimal growth trajectories with finite carrying capacity
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevE.94.022315
Publisher version: https://doi.org/10.1103/PhysRevE.94.022315
Language: English
Additional information: Copyright © 2016 American Physical Society. The published version of record is available at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.022315
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1502786
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