Logarithmic Utility

Optimal Diversification and Leverage in a Utility-Based Portfolio Allocation Approach ArXiv ID: 2503.07498 “View on arXiv” Authors: Unknown Abstract We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance existing methodologies by incorporating compound probability distributions to model the effects of both statistical and non-stationary uncertainties. Additionally, we extend the maximum expected utility objective by including the variance of utility in the objective function, which we term generalized mean-variance. In the case of logarithmic utility, it provides a natural explanation for the half-Kelly criterion, a concept widely used by practitioners. ...

Application of the Kelly Criterion to Prediction Markets ArXiv ID: 2412.14144 “View on arXiv” Authors: Unknown Abstract Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified payout structure is proposed. A simple asset price model based on flipping biased coins is investigated. It is shown using the Kullback-Leibler divergence how the misjudgment of the bias and the miscalculation of the investment fraction influence the portfolio growth rate. ...