Weighted Entropy and Optimal Portfolios for Risk-averse Kelly Investments

Authors

M. Kelbert, Moscow Higher School of Economics
I. Stuhl, University of Denver, IMS, University of Sao Paulo, University of Debrecen
Y. Suhov, Penn State University, DPMMS, University of Cambridge, IPIT RAS

Publication Date

11-11-2017

Document Type

Article

Organizational Units

Mathematics

Keywords

Capital growth investment, Supermartingale, Optimal portfolios, Weighted entropy

Abstract

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes ‘weights’ of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.

Publication Statement

Copyright held by author or publisher. User is responsible for all copyright compliance.

Recommended Citation

Kelbert, M, et al. “Weighted Entropy and Optimal Portfolios for Risk-Averse Kelly Investments.” Aequationes Mathematicae, vol. 92, no. 1, 2018, pp. 165–200. doi: 10.1007/s00010-017-0515-6.