Robust investment strategies with discrete asset choice constraints using DC programming

Abstract

In this article, we are concerned with robust investment strategies for the portfolio management problem. We extend the classical Markowitz framework with discrete asset choice constraints to worst-case portfolio selection with rival risk and return scenario specifications. Robustness is ensured by considering the optimal strategy in view of multiple rival scenarios and evaluating the portfolio simultaneously with the worst-case scenario. Discrete constraints, such as buy-in thresholds and cardinality, represent the investor's choice on the assets. Portfolio allocation with discrete asset choice constraints is a non-convex and NP-hard problem. A local deterministic optimization approach based on difference of convex (DC) functions programming is introduced and a DC algorithm (DCA) is developed to solve min–max mean–variance portfolio optimization problem. The computational results using historical data show that the DCA is more efficient than the standard methods and often provides a global solution.

Keywords:

• DC programming
• DCA
• worst-case analysis
• mean–variance portfolios

AMS Subject Classifications:

• 90C11
• 90C26
• 91B28