During the past fifty years, portfolio optimization has been a central theme in quantitative finance: one is essentially looking for the right compromise between risk and return on investment.
Recently, we have moved away from Markowitz’ classical variance versus mean return based performance functions, to quantile based risk measures (risk capital and variants), but also to robust models which explicitly account for uncertainty in the financial data (Goldfarb and Lyengar, M.O.R. 2003, El Gahoui, Oks and Oustry, O.R. 2003).
In this joint work with my master student Simon-Carl Dunberry, we compare the above two robust approaches and demonstrate their advantages relative to non robust approaches.