Gambling and R\'enyi Divergence
Information Theory
2019-04-29 v2 math.IT
Abstract
For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly's logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the R\'enyi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional R\'enyi divergence.
Keywords
Cite
@article{arxiv.1901.06278,
title = {Gambling and R\'enyi Divergence},
author = {Cédric Bleuler and Amos Lapidoth and Christoph Pfister},
journal= {arXiv preprint arXiv:1901.06278},
year = {2019}
}
Comments
6 pages; accepted at ISIT 2019; with additional proofs