optimalPoisson: Kelly-fraction under geometric compensated Poisson dynamics

In shill1729/kellyfractions: Optimize log returns

Kelly-fraction under geometric compensated Poisson dynamics

Description

Generate a sample path of \log X_t of the Kelly portfolio under a stock driven by a geometric compensated Poisson process.

Usage

optimalPoisson(tt, a, b, lambda, rate = 0, N = 1000)

Arguments

tt	maturity to simulate until
a	jump size
b	compensator size
lambda	mean-rate of jumps
rate	risk-free rate of return
N	number of time-subintervals to take

Details

The optimal fraction is analytically known through the equation \lambda/(r+b)-1/(e^a-1) where the log dynamics follow X_t=aN_t-bt, a scaled and compensated Poisson process. A basic Euler-Maruyama scheme is then used to generate sample paths of both the stock and the Kelly-portfolio.

Value

data.frame of time, stock, and the portfolio values.

shill1729/kellyfractions documentation built on July 16, 2025, 6:21 p.m.