Utility Theory

Risk Limited Asset Allocation with a Budget Threshold Utility Function and Leptokurtotic Distributions of Returns ArXiv ID: 2512.11666 “View on arXiv” Authors: Graham L Giller Abstract An analytical solution to single-horizon asset allocation for an investor with a piecewise-linear utility function, called herein the “budget threshold utility,” and exogenous position limits is presented. The resulting functional form has a surprisingly simple structure and can be readily interpreted as representing the addition of a simple “risk cost” to otherwise frictionless trading. ...

Dynamically optimal portfolios for monotone mean–variance preferences ArXiv ID: 2503.08272 “View on arXiv” Authors: Unknown Abstract Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the moments of asset returns. We interpret the maximal MMV utility in terms of the monotone Sharpe ratio (MSR) and show that the global squared MSR arises as the nominal yield from continuously compounding at the rate equal to the maximal local squared MSR. The paper gives simple necessary and sufficient conditions for mean-variance (MV) efficient portfolios to be MMV efficient. Several illustrative examples contrasting the MV and MMV criteria are provided. ...

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. ...