Optimal portfolio trading subject to stochastic dominance constraints under second‐order autoregressive price dynamics

• Published in: International transactions in operational research Vol. 27; no. 3; pp. 1771 - 1803
• Main Authors: Singh, Arti, Dharmaraja, Selvamuthu
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2020
• Subjects: autoregressive behavior; Autoregressive models; Computational geometry; Constraints; convex programming; Convexity; Economic models; execution cost; Mathematical programming; Mutual funds; Operations research; optimal trading; Optimization; Quadratic programming; Risk; risk aversion; stochastic dominance
• ISSN: 0969-6016; 1475-3995
• DOI: 10.1111/itor.12435

This paper studies the optimal portfolio trading problem under the generalized second‐order autoregressive execution price model. The problem of minimizing expected execution cost under the proposed price model is formulated as a quadratic programming (QP) problem. For a risk‐averse trader, problem formulation under the second‐order stochastic dominance constraints results in a quadratically constrained QP problem. Under some conditions on the execution price model, it is proved that the portfolio trading problems for risk‐neutral and risk‐averse traders become convex programming problems, which have many theoretical and computational advantages over the general class of optimization problems. Extensive numerical illustrations are provided, which render the practical significance of the proposed execution price model and the portfolio trading problems.