Mixed-Integer Linear Programming (MILP)

Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspective ArXiv ID: 2509.22896 “View on arXiv” Authors: Peng Xu Abstract This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to capture all reverse S-shaped MSD preferences as well as all subjective decision weights generated by inverse S-shaped probability weighting functions. We demonstrate that these dominance conditions can be admitted as linear constraints into the stochastic optimization problems to formulate computationally tractable mixed-integer linear programming (MILP) models. We then employ the developed MILP models in financial portfolio analysis and examine classic behavioral factors such as reference point and subjective probability distortion in behavioral investors’ portfolio decisions. ...

Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach ArXiv ID: 2401.02601 “View on arXiv” Authors: Unknown Abstract We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation. ...

A new behavioral model for portfolio selection using the Half-Full/Half-Empty approach ArXiv ID: 2312.10749 “View on arXiv” Authors: Unknown Abstract We focus on a behavioral model, that has been recently proposed in the literature, whose rational can be traced back to the Half-Full/Half-Empty glass metaphor. More precisely, we generalize the Half-Full/Half-Empty approach to the context of positive and negative lotteries and give financial and behavioral interpretations of the Half-Full/Half-Empty parameters. We develop a portfolio selection model based on the Half-Full/Half-Empty strategy, resulting in a nonconvex optimization problem, which, nonetheless, is proven to be equivalent to an alternative Mixed-Integer Linear Programming formulation. By means of the ensuing empirical analysis, based on three real-world datasets, the Half-Full/Half-Empty model is shown to be very versatile by appropriately varying its parameters, and to provide portfolios displaying promising performances in terms of risk and profitability, compared with Prospect Theory, risk minimization approaches and Equally-Weighted portfolios. ...