AMS Seminar: Thalia Zariphopoulou (University of Texas) @ Whitehead 304

Title: “Real-time” optimization under forward rank-dependent processes: time-consistent optimality under probability distortions
Abstract: Forward performance processes are defined via time-consistent optimality and incorporate “real-time” incoming information. On the other hand, popular performance criteria – for example, mean-variance optimization, hyperbolic discounting, probability distortions – are by nature time-inconsistent. How to define forward performance criteria in time-inconsistent settings then becomes a challenging problem, both conceptually and technically. In this talk, I will discuss the case of probability distortions and introduce the concept of forward rank-dependent performance processes. Among others, I will show how forward probability distortions are affected by “real-time” changes in the stochastic environment and, also, present a striking equivalence between forward rank-dependent criteria and time-monotone forward processes under appropriate measure-changes. A byproduct of the work is a novel result on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.