On the criterion vectors of lines of portfolio selection with multiple quadratic and multiple linear objectives

Abstract

As the research for portfolio selection evolves, traditional models and models with one quadratic objective and multiple linear objectives are being solved. In this paper, I propose models with multiple quadratic and multiple linear objectives. Due to the difficulty involved, I study the new models by lines in decision space, analyze the criterion vectors of the lines by projection, and approximate the nondominated sets by the criterion vectors. As an illustration, I extend Merton's portfolio selection model, propose algorithms to approximate the nondominated sets by the criterion vectors of portfolios with cardinality 3 and then K , and demonstrate the number of the criterion vectors.

On convex multiobjective programs with application to portfolio optimization

“…The model uses a perturbed covariance matrix being the sum of the covariance matrix and a symmetric perturbation matrix that is built from the diagonal elements of the covariance matrix. Another model leading to quadratic functions results from the variance of portfolio liquidity (Qi, 2017). In all these models, the goal is to find the set of efficient portfolios and the set of their Pareto performances.…”

“…The first one is perhaps the derivation for the biobjective case by Merton (1972), which is followed by Qi et al (2017) for the triobjective case with one quadratic and two linear objective functions. This work is extended by Qi (2017) to any number of quadratic and linear functions and is the first analytical study addressing the multiobjective portfolio optimization problem (MOPOP) with more than one quadratic objective function. This goes along with Markowitz (2013), Boyd et al (2017), and Salas-Molina et al (2018) who recognize the need to model different types of risk measures, which naturally may lead to several quadratic functions in the MOPOP model.…”