Speaker: Gabriela Kovacova
Date & Time: December 3, 2021, Friday, 13:30
Place: EE – 01
Title: The set-valued Bellman principle
Abstract: Dynamic programming and the Bellman equation have a variety of applications not only in finance, but in many other scientific fields as well. While multivariate problems of optimal control have been solved via dynamic programming in the past, an explicit form of the Bellman equation has not been available until now. We use the lattice approach to vector optimization to derive it. As it is based on a set optimization notion of infimum, we call it a set-valued Bellman principle. We study this principle in the context of the mean-risk problem, treated as a multi-objective optimization problem. As such, the mean-risk problem turns out to be time consistent (in a manner appropriate for a multi-objective optimization problem) and to satisfy the set-valued Bellman principle. One open challenge is practical implementation of the set-valued Bellman principle since it requires us to solve parametrized multi-objective optimization problems. Since projection problems appear to be a promising approach, we also study convex projections and their connection to convex multi-objective optimization.
Bio: Gabriela Kovacova has just finished her PhD studies at the Institute for Statistics and Mathematics at Vienna University of Economics and Business, Austria. Her research interests include dynamic multivariate programming, vector optimization and financial mathematics.