Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Wednesday, January 11, 2017 - 16:00 in V3-201

Robust Markowitz mean-variance portfolio selection under ambiguous volatility and correlation

A talk in the 'Bielefeld Stochastic Afternoon - Math Finance Session' series by
Huyen Pham from University Paris Diderot
Abstract: The Markowitz mean-variance portfolio selection problem is the cornerstone of modern portfolio allocation theory. In this talk, we study a robust continuous time version of the Markowitz criterion when the model uncertainty carries on the variance-covariance matrix of the risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies in the case of uncertain volatilities and ambiguous correlation between two risky assets, and then derive the robust efficient frontier in closed-form. We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy, and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.