Book of Abstracts

EPCO 2021 book of abstracts is now available for download

epco_2021_book_of_abstracts.pdf

Invited Speakers

Professor Agnès Sulem (INRIA Paris, France)

Title: Mean-field BSDEs with jumps and global risk measures

Abstract: We study mean-field Backward Stochastic Differential Equations with jumps, when the drift  contains  a generalized mean-field operator that can capture higher order interactions. Indeed, in many applications (and specifically in interacting systems), it may be desirable to incorporate the intensity of system interactions as well, and not only the average state. We  interpret  the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system. This influence can come in a wide class of choices,  including the average system state or average intensity of system interactions. We provide convergence results of finite interacting systems to the limit mean-field BSDE. We state properties for the mean-field BSDE, in particular  a strict comparison theorem which is used to verify the no arbitrage condition of our global risk measure. Furthermore, using Fenchel-Legendre transforms, we prove a dual representation for the expectation of the associated global risk measure. 

Talk based on joint works with Zhongyuan Cao (INRIA Paris), Rui Chen (INRIA Paris), Roxana Dumitrescu (King's College London), Andreea Minca (Cornell University). 

Short Bio

Agnès Sulem is a researcher at the Paris Research Center of INRIA, the French National Institute for Computer Science and Applied Mathematics, and leads the "MATHRISK'' research group on stochastic analysis and financial mathematics (https://www.inria.fr/en/teams/mathrisk). She is also the director of the Premia consortium, which provides a numerical platform for quantitative finance. (http://www.premia.fr). Agnès Sulem is teaching in the doctoral program at the University of Luxemburg. Her fields of research are stochastic control, numerical and stochastic analysis, and mathematical finance. She is the author of 2 books (in 2019 has appeared the 3^rd edition of her book “Applied Stochastic Control of Jump diffusions” with Bernt Øksendal, Springer, Universitext), and about 100 research articles and has been supervising a dozen of PhD theses. She is a member of the Editorial Boards of SIAM Journal on Financial Mathematics and the Journal of Mathematical Analysis and Applications, and is a reviewer for Mathematical Reviews.

Agnès Sulem studied at “Pierre and Marie Curie” Paris University and obtained her PhD in Mathematics under the supervision of Prof. Alain Bensoussan and her «Habilitation pour diriger des recherches» from the University Paris-Dauphine.

Agnès Sulem has been awarded the title of “Chevalier de l’Ordre de la Légion d’Honneur” for her scientific career. Besides mathematics, Agnès Sulem enjoys playing the violin.

Professor Michael Ulbrich (Technical University of Munich, Germany)

Title: An interior point approach for risk-averse PDE-constrained optimization with coherent risk measures

Abstract: The prevalence of uncertainty in models of engineering and the natural sciences necessitate the inclusion of random parameters in the underlying partial differential equations (PDEs). The resulting decision problems governed by the solution of such random PDEs are infinite dimensional stochastic optimization problems. In order to obtain risk-averse optimal decisions in the face of such uncertainty, it is common to employ risk measures in the objective function. This leads to risk-averse PDE-constrained optimization problems. We propose a method for solving such problems in which the risk measures are convex combinations of the mean and conditional value-at-risk (CVaR). Since these risk measures can be evaluated by solving a related inequality-constrained optimization problem, we propose a log-barrier technique to approximate the risk measure, which leads to a new continuously differentiable convex risk measure: the log-barrier risk measure. We  prove consistency of the approximation via a variational convergence technique. Using the differentiability of the log-barrier risk measure, we derive first-order optimality conditions reminiscent of interior point approaches in nonlinear programming. We study the associated Newton systems in full and reduced form and provide a sufficient condition for local superlinear convergence in the continuous setting. For the discretization of the problem, we employ novel low-rank tensor methods. The presentation concludes with numerical examples.

This is joint work with Sebastian Garreis and Thomas Surowiec.

Short Bio

Michael Ulbrich is Professor of Mathematics and Director of the Chair of Mathematical Optimization at the Technical University of Munich (TUM), Germany, since 2006. From 2007 to 2010, he served as the Dean of Academic Affairs and 2012-2015 as the Vice Dean of the Department of Mathematics at TUM. He is a secondary member of the Department of Informatics. Before joining TUM, he was a Professor at the University of Hamburg (2002-2006) and the Coordinator of the Center for Optimization and Approximation (2003-2006). Funded by the German Research Foundation (DFG), he spent extended research stays at Rice University, Houston, TX in 1996/97 and 1999/2000. In 1996 he received his doctorate and in 2002 his Habilitation at TUM.

The research of Michael Ulbrich centers on the theory, numerical methods, and applications of large-scale nonlinear optimization, PDE-constrained optimization and control, variational inequalities, and nonsmooth problems. His work is often related to applications, e.g., in the context of shape optimization and control of fluid flows, parameter identification, or the analysis of human motion. Michael Ulbrich is a PI and a member of the Steering Committee of the DFG Priority Program SPP 1962 ``Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization'' and a PI of the DFG/FWF International Research Training Group IGDK 1754 Munich-Graz ``Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures''.

He has published two monographs in the field of PDE-constrained optimization (MOS-SIAM and Springer) and an introductory book on nonlinear optimization (Springer). Michael Ulbrich received the Howard Rosenbrock Prize 2015 (with M. Simon). He serves on the editorial boards of Mathematical Programming Computation, SIAM Journal on Scientific Computing, Optimization and Engineering, and Numerical Algebra, Control and Optimization.