Robust multiobjective portfolio optimization: a set order relations approach

Abstract

We consider Markowitz’s portfolio optimization problem that heavily suffers from uncertainties of input parameters. And based on set order relations, uncertain portfolio optimization problem at various extreme cases is modelled as robust multiobjective formulations. At first, borrowing set order relations, three concepts of set less ordered efficiency are defined for multiobjective portfolio optimization problems with uncertainties. Subsequently, following from Ben-Tal and Nemirovski (Math Oper Res 23(4):769–805, 1998; Oper Res Lett 25:1–13, 1999), several multiobjective robust counterparts are introduced, and tackled by multiobjective particle swarm optimization approach. As such, the properties of the obtained (robust) efficient solutions are further characterized. Finally, the empirical researches from the real stock market show that (robust) efficient solutions based on set order relations are highly advisable for the investors.