Computing Discrete Expected Utility Maximizing Portfolios

Posted: 23 Aug 2010 Last revised: 31 Oct 2014

Sarah Drewes

University of California, Berkeley, Industrial Engineering and Operations Research

Sebastian Pokutta

Georgia Institute of Technology

Date Written: August 20, 2010

Abstract

Maximizing the expected logarithmic utility, or equivalently the geometric mean, of a portfolio is a well-known yet controversially discussed objective. Nonetheless, it is an often used objective function for computing real-world portfolios and in particular it met a great amount of sympathy in the alternative investment industry. In the purely continuous case the resulting portfo- lio optimization problem can be solved using methods from convex optimization rather efficiently. However, In reality we often face discrete decisions, e.g., setting up a new venture, acquisitions, mergers, where approximation by a continuous variable is inappropriate. We will focus on how to solve the utility maximization problem in the presence of discrete decisions, in particular allowing for the inclusion of transaction costs and fixed charges. We demonstrate the efficiency of our approach by computational experiments for large-scale portfolios showing the applicability and we present a brief backtesting experiment conducted for the German stock market. Our approach generalizes to other utility functions satisfying some mild requirements.

Keywords: expected logarithmic utility, optimization, SQP, outer approximation, kelly criterion, geometric mean maximization, discrete decisions

JEL Classification: G11, C61, C63, D80

Suggested Citation

Drewes, Sarah and Pokutta, Sebastian, Computing Discrete Expected Utility Maximizing Portfolios (August 20, 2010). Available at SSRN: https://ssrn.com/abstract=1662729 or http://dx.doi.org/10.2139/ssrn.1662729

Sarah Drewes

University of California, Berkeley, Industrial Engineering and Operations Research ( email )

Berkeley, CA 94720
United States

Sebastian Pokutta (Contact Author)

Georgia Institute of Technology ( email )

Atlanta, GA 30332
United States

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