Optimal growth trajectories with finite carrying capacity

F. Caravelli, L. Sindoni, F. Caccioli, C. Ududec

Physical Review E 94, 22315 (2016)


Download the PDF

LQ placeholderIn presence of a finite carrying capacity, it is crucial to identify optimal strategies for maximal growth.

In presence of a finite carrying capacity, it is crucial to identify optimal strategies for maximal growth.

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.

LQ placeholder

Scale of non-locality for a system of n particles

S. Talaganis, I. Teimouri

Sub. to Physical Review D

LQ placeholder

How much can we influence the rate of innovation?

T. Fink, M. Reeves

Science Advances

LQ placeholder

The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

Nature Reviews Physics

LQ placeholder

On defining the Hamiltonian beyond quantum theory

D. Branford, O. Dahlsten, A. Garner

Foundations of Physics

LQ placeholder

Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy

R. Farr, Z. Vukmanovic, M. Holness, E. Griffiths

Physical Review Materials

LQ placeholder

Tackling information asymmetry in networks: a new entropy-based ranking index

P. Barucca, G. Caldarelli, T. Squartini

Journal of Statistical Physics

LQ placeholder

Eigenvalues of subgraphs of the cube

B. Bollobás, J. Lee, S. Letzter

European Journal of Combinatorics

LQ placeholder

Maximum one-shot dissipated work from Rényi divergences

N. Halpern, A. Garner, O. Dahlsten, V. Vedral

Physical Review E

123 / 123 papers