Forecasting the propagation of pandemic shocks with a dynamic input-output model
Pichler, A Pangallo, M Del Rio-Chanona, R Lafond, F Farmer, J Journal of Economic Dynamics and Control volume 144 (13 Sep 2022)
Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces
Kramkov, D Sîrbu, M (10 Sep 2022)
Multilevel Path Branching for Digital Options
Giles, M Haji-Ali, A (07 Sep 2022)
Relativity of superluminal observers in $1+3$ spacetime
Dragan, A Dębski, K Charzyński, S Turzyński, K Ekert, A (05 Sep 2022)
Nonlinear electrochemical impedance spectroscopy for lithium-ion battery model parameterization
Kirk, T Lewis-Douglas, A Howey, D Please, C Chapman, S (08 Sep 2022)
Desperately searching for something
Bowman, C Grindrod, P Communications in Nonlinear Science and Numerical Simulation volume 125 (08 Jun 2023)
Direct products of free groups in ${{\rm{Aut}}}(F_N)$
Bridson, M Wade, R (02 Sep 2022)
Thu, 27 Oct 2022

16:00 - 17:00
L3

Merton's optimal investment problem with jump signals

Laura Körber (Berlin)
Abstract

This talk presents a new framework for Merton’s optimal investment problem which uses the theory of Meyer $\sigma$-fields to allow for signals that possibly warn the investor about impending jumps. With strategies no longer predictable, some care has to be taken to properly define wealth dynamics through stochastic integration. By means of dynamic programming, we solve the problem explicitly for power utilities. In a case study with Gaussian jumps, we find, for instance, that an investor may prefer to disinvest even after a mildly positive signal. Our setting also allows us to investigate whether, given the chance, it is better to improve signal quality or quantity and how much extra value can be generated from either choice.
This talk is based on joint work with Peter Bank.

Thu, 13 Oct 2022

16:00 - 17:00
L3

MF-OMO: An Optimization Formulation of Mean-Field Games

Anran Hu
Abstract

Theory of mean-field games (MFGs) has recently experienced an exponential growth. Existing analytical approaches to find Nash equilibrium (NE) solutions for MFGs are, however, by and large restricted to contractive or monotone settings, or rely on the uniqueness of the NE. We propose a new mathematical paradigm to analyze discrete-time MFGs without any of these restrictions. The key idea is to reformulate the problem of finding NE solutions in MFGs as solving an equivalent optimization problem, called MF-OMO (Mean-Field Occupation Measure Optimization), with bounded variables and trivial convex constraints. It is built on the classical work of reformulating a Markov decision process as a linear program, and by adding the consistency constraint for MFGs in terms of occupation measures, and by exploiting the complementarity structure of the linear program. This equivalence framework enables finding multiple (and possibly all) NE solutions of MFGs by standard algorithms such as projected gradient descent, and with convergence guarantees under appropriate conditions. In particular, analyzing MFGs with linear rewards and with mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This optimization reformulation of MFGs can be extended to variants of MFGs such as personalized MFGs.

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