Dear Colleagues and Students,
You are invited to a series of five seminars on Financial Mathematics in Spring 2019.
The second seminar is on 16 April 2019, Tuesday. Here is the detailed information.
Title: Dynamic Multivariate Programming
Speaker: Birgit Rudloff, Vienna University of Economics and Business, Vienna, Austria
Date/Place: 16 April 2019, Tuesday, 13:40, EA-409
In this talk, I present a set-valued Bellman principle. As a first example, a famous vector optimization problem is considered: the dynamic mean-risk portfolio optimization problem. Usually, this problem is scalarized and it is well known that this problem does not satisfy the (scalar) Bellman principle. However, when we leave it in its original form as a vector optimization problem, the upper images, whose boundary is the efficient frontier, recurse backwards in time . Conditions are presented under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. As a second example, the set-valued Bellman principle appears when considering time consistency of multivariate risk measures. Similar to the first example, one can show that a (fixed) scalarization of the problem does not satisfy the (scalar) Bellman principle, but a particular moving scalarization leads also to scalar time consistency [2, 1]. This is an observation also made in , but with our approach this moving scalarization is part of the solution and not needed as an input.
References: Z. Feinstein, B. Rudloff (2018): Time consistency for scalar multivariate risk measures. Submitted for publication.  Z. Feinstein, B. Rudloff (2018): Scalar multivariate risk measures with a single eligible asset. Submitted for publication.  Ch. Karnam, J. Ma, J. Zhang (2017): Dynamic approaches for some time- inconsistent optimization problems. The Annals of Applied Probability, 27(6), 3435 – 3477.  G. Kovacova, B. Rudloff (2018): Time consistency of the mean-risk problem. Submitted for publication.
Bio: Birgit Rudloff is full professor for “Mathematics for Economics and Business” at the Vienna University of Economics and Business. Before coming to Vienna, she was an Assistant Professor at Princeton University, at the Department for Operations Research and Financial Engineering and at the Bendheim Center for Finance. She holds a PhD in Financial Mathematics from Martin-Luther University of Halle-Wittenberg in Germany. Her research is centered around multivariate risks. She works on measuring and regulating systemic risk in banking networks, dynamic risk measures in markets with transaction costs and on multivariate dynamic optimization problems. In her recent research she developed a dynamic programming principle (Bellman principle) for multivariate dynamic optimization problems, that can be used e.g. to solve the mean-risk portfolio optimization problem.