We revisit portfolio selection models by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by optimal transport costs. In many cases, this problem can be simplified into an empirical risk minimization problem with a regularization term. Moreover, we extend a recently developed inference methodology in order to select the size of the distributional uncertainty in a data-driven way. Our formulations allow us to inform the distributional uncertainty region using market information (e.g. via implied volatilities). We provide substantial empirical tests that validate our approach.
(This presentation is based on the following papers: https://arxiv.org/pdf/1802.04885.pdf and https://arxiv.org/abs/1810.02403.)
- Stochastic Analysis & Mathematical Finance Seminars