| Title |
Optimal growth trajectories with finite carrying capacity
|
|---|---|
| Published in |
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, August 2016
|
| DOI | 10.1103/physreve.94.022315 |
| Pubmed ID | |
| Authors |
F Caravelli, L Sindoni, F Caccioli, C Ududec |
| 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. |
X Demographics
The data shown below were collected from the profiles of 6 X users who shared this research output. Click here to find out more about how the information was compiled.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Puerto Rico | 1 | 17% |
| United States | 1 | 17% |
| Unknown | 4 | 67% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 6 | 100% |
Mendeley readers
The data shown below were compiled from readership statistics for 15 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| France | 1 | 7% |
| Unknown | 14 | 93% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Researcher | 3 | 20% |
| Student > Master | 3 | 20% |
| Student > Ph. D. Student | 2 | 13% |
| Student > Doctoral Student | 1 | 7% |
| Unknown | 6 | 40% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 3 | 20% |
| Physics and Astronomy | 3 | 20% |
| Agricultural and Biological Sciences | 1 | 7% |
| Engineering | 1 | 7% |
| Unknown | 7 | 47% |
Attention Score in Context
This research output has an Altmetric Attention Score of 6. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 26 April 2020.
All research outputs
#6,280,178
of 25,385,509 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#1,899
of 20,990 outputs
Outputs of similar age
#92,831
of 354,307 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#23
of 373 outputs
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