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.
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
#6,743,823
of 26,794,105 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#2,036
of 21,579 outputs
Outputs of similar age
#90,066
of 336,359 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#25
of 372 outputs
Altmetric has tracked 26,794,105 research outputs across all sources so far. This one has received more attention than most of these and is in the 74th percentile.
So far Altmetric has tracked 21,579 research outputs from this source. They receive a mean Attention Score of 3.1. This one has done particularly well, scoring higher than 90% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 336,359 tracked outputs that were published within six weeks on either side of this one in any source. This one has gotten more attention than average, scoring higher than 73% of its contemporaries.
We're also able to compare this research output to 372 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 93% of its contemporaries.
