Weighted entropy and optimal portfolios for risk-averse Kelly investments

M. Kelbert; I. Stuhl; Y. Suhov

doi:10.1007/s00010-017-0515-6

Weighted entropy and optimal portfolios for risk-averse Kelly investments

M. Kelbert, I. Stuhl, Y. Suhov

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	165-200
Number of pages	36
Journal	Aequationes Mathematicae
Volume	92
Issue number	1
DOIs	https://doi.org/10.1007/s00010-017-0515-6
State	Published - Feb 1 2018

All Science Journal Classification (ASJC) codes

Mathematics(all)
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes {\textquoteleft}weights{\textquoteright} 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.",

author = "M. Kelbert and I. Stuhl and Y. Suhov",

note = "Funding Information: The authors are grateful to their respective institutions for the financial support and hospitality: MK thanks the Higher School of Economics for the support in the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Programme; IS was supported by the FAPESP Grant No 11/51845-5, and thanks the IMS, USP and to Math Dept, University of Denver; YS thanks the Math Dept, PSU. Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.",

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AU - Suhov, Y.

N1 - Funding Information: The authors are grateful to their respective institutions for the financial support and hospitality: MK thanks the Higher School of Economics for the support in the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Programme; IS was supported by the FAPESP Grant No 11/51845-5, and thanks the IMS, USP and to Math Dept, University of Denver; YS thanks the Math Dept, PSU. Publisher Copyright: © 2017, Springer International Publishing AG.

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N2 - 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.

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Weighted entropy and optimal portfolios for risk-averse Kelly investments

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