Seminar: Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion

Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Date: Friday, September 11, 2020, 16:30 to 17:30
Title: Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion
Speaker: Professor Moris Strub (Southern University of Science and Technology)
We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions.  For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or  the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, “distorted” measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. Finally, our results on forward rank-dependent performance criteria motivate us to revisit the classical (backward) setting. We follow the so-called dynamic utility approach and derive conditions for existence and a construction of dynamic rank-dependent utility processes.
Moris Strub is an assistant professor at the Department of Information Systems and Management Engineering of the SUSTech College of Business. He has obtained a BSc in Mathematics and MSc in Applied Mathematics from ETH Zurich, both with distinction, and a PhD in Financial Engineering from the Chinese University of Hong Kong. Before joining SUSTech, he was a Postdoctoral Fellow at the Chinese University of Hong Kong and a Staff Associate at Columbia University. Moris main research interests are in the areas of Portfolio Selection, Behavioral Finance and Economics, Mathematical Finance, Risk Management, and Robo-Advising.
Friday, September 11, 2020 - 16:30 to 17:30