kellyfractions

The package kellyfractions provides functions for computing log-optimal wagers, bets, allocations, and portfolios under a variety of models of increasing generality. Features also include simulations of each model and the growth-rates obtained from each strategy.

Installation

You can install the latest version of kellyfractions from github via the devtools package:

devtools::install_github("shill1729/kellyfractions")

Examples of optimal sample paths

How to do simulations:

Binary wagers

library(kellyfractions)
# +/- $1 bets at 0.6 chance
samplepath <- optimalBinary(bankroll = 1000, p = 0.6, a = 1, b = 1)
plot(samplepath, type = "l", main = "Binary wagers")

Testing solution accuarcy

Here we compare three methods that should coincide for the special case of cev=1.

library(kellyfractions)
mu <- 0.10
volat <- 0.25
rate <- 0
cev <- 1
dynamics <- list(drift = function(t, s) mu,
                 diffusion = function(t, s) volat*s^(cev-1)
)
# Optimal allocations
kito <- kellyItoProcess(0, s = 100, dynamics, rate)
kgbm <- kellyGBM(mu, volat, rate)
kcev <- kellyCEV(spot = 100, rate, parameters = c(mu, volat, cev))

# Growth rates under optimal strategies
gito <- entropyItoProcess(t = 1, s = 100, dynamics = dynamics, rate)
ggbm <- entropyGBM(mu, volat, rate)
gcev <- entropyCEV(t = 1, spot = 100, rate = rate, parameters = c(mu, volat, cev))

# These should be approximately equal
output <- rbind(c(kgbm, kito, kcev),
                c(ggbm, gito, gcev)
)
colnames(output) <- c("gbm", "ito", "cev")
rownames(output) <- c("fraction", "growth")
print(output)