Dynamic Mean-Variance Problem: Recovering Time-Consistency
April 13, 2023 | 5:00 - 6:00 PM | Babbio 2nd Floor Room 219
The dynamic mean-variance problem is a well-studied optimization problem that is known to be time-inconsistent. The main source of time- inconsistency is that the family of conditional variance functionals indexed by time fails to be recursive. We consider the mean-variance problem in a discrete-time setting and study an auxiliary dynamic vector optimization problem whose objective function consists of the conditional mean and conditional second moment.
We show that the vector optimization problem satisfies a set-valued dynamic programming principle and is time-consistent in a generalized sense. Moreover, its weighted sum scalarizations are closely related to the mean-variance problem through simple nonlinear transformations. This is at the cost of using stochastic and time-varying weights in the mean-variance problem. We also discuss the relationship between our results and some recent results in the literature that discuss the use of time-varying weights under special dynamics. Finally, in a finite probability space, we propose a computational procedure that relies on convex vector optimization and convex projection problems, and we use this procedure to calculate time- consistent solutions in concrete market models. Joint work with Seyit Emre Düzoylum (UC Santa Barbara).
Çağın Ararat is an Assistant Professor in the Department of Industrial Engineering at Bilkent University. He received his BSc degree in 2010 from the same department, followed by a PhD degree in 2015 from the Department of Operations Research and Financial Engineering at Princeton University. His research interests include risk measures, systemic risk, set-valued stochastic analysis and backward stochastic differential equations. During the academic year 2022-2023, he is on sabbatical leave and visiting the Department of Mathematics at the University of Southern California as a Fulbright Scholar.