In this talk we introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure.

Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

This talk is based on joint work with Julian Sester and Mario Sikic.

The corresponding papers can be found here:

Ariel Neufeld is a Nanyang Assistant Professor in mathematics at the Nanyang Technological University in Singapore. He received his PhD in mathematics in May 2015 at ETH Zurich, where he spent half of his PhD at the Columbia University in the City of New York. Prior to joining NTU he was a postdoctoral researcher at ETH Zurich. His research focuses on model uncertainty in financial markets and distributionally robust optimization, machine learning algorithms and their applications in finance and insurance, financial and insurance mathematics, as well as stochastic analysis and stochastic optimal control.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg