Title

Weighted Entropy and Optimal Portfolios for Risk-averse Kelly Investments

Document Type

Article

Publication Date

11-11-2017

Keywords

Capital growth investment, Supermartingale, Optimal portfolios, Weighted entropy

Organizational Units

College of Natual Science and Mathematics, Mathematics

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

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