Computing Discrete Expected Utility Maximizing Portfolios

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