A reformulation of a mean-absolute deviation portfolio optimization model
Management Science
Computing efficient frontiers using estimated parameters
Annals of Operations Research
Computational study of a family of mixed-integer quadratic programming problems
Mathematical Programming: Series A and B
A Computational Study of Search Strategies for Mixed Integer Programming
INFORMS Journal on Computing
Robust portfolio selection problems
Mathematics of Operations Research
Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse
SIAM Journal on Optimization
Mathematical Programming: Series A and B
Perspective cuts for a class of convex 0–1 mixed integer programs
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Convexity of chance constraints with independent random variables
Computational Optimization and Applications
A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs
INFORMS Journal on Computing
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
Capital rationing problems under uncertainty and risk
Computational Optimization and Applications
Game Theoretical Approach for Reliable Enhanced Indexation
Decision Analysis
Journal of Global Optimization
Construction of Risk-Averse Enhanced Index Funds
INFORMS Journal on Computing
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In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint, which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs and give closed-form formulations. Second, we account for real-world trading constraints (such as the need to diversify the investments in a number of industrial sectors, the nonprofitability of holding small positions, and the constraint of buying stocks by lots) modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a nonlinear branch-and-bound algorithm that features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and is called portfolio risk branching. The two branching rules are implemented and tested using the open-source Bonmin framework. The comparison of the computational results obtained with state-of-the-art MINLP solvers (MINLP_BB and CPLEX) and with our approach shows the effectiveness of the latter, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time. The practicality of the approach is illustrated through its use for the construction of four fund-of-funds now available on the major trading markets.