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March 2023

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Seminario di Markus Fischer - 7 marzo, Sapienza Università di Roma
by Giacomo Di Gesu 02 Mar '23

02 Mar '23

Martedì 7 marzo, ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma. *Speaker: *Markus Fischer, Università di Padova *Title: *On correlated equilibria and mean field games *Abstract: *Mean field games are limit models for symmetric N-player games, as the number of players N tends to infinity. The prelimit models are usually solved in terms of Nash equilibria. A generalization of the notion of Nash equilibrium, due to Robert Aumann (1974, 1987), is that of correlated equilibrium. In a simple discrete setting, we will discuss correlated equilibria for mean field games and their connection with the underlying N-player games. We first consider equilibria in restricted strategies (Markov open-loop), where control actions depend only on time and a player's own state. In this case, N-player correlated equilibria are seen to converge to the mean field game limit and, conversely, correlated mean field game solutions induce approximate N-player correlated equilibria. We then discuss the problem of constructing approximate equilibria when deviating players have access to the aggregate system state. We also give an explicit example of a correlated mean field game solution not of Nash-type. Results (with L. Campi and Federico Cannerozzi) on a related notion of equilibrium in a diffusion-type setting will be mentioned as well. Joint work with Ofelia Bonesini (Imperial College London) and Luciano Campi (University of Milan "La Statale")

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Seminar Prof. Kostas Kardaras on "Portfolio choice under taxation and time constraints", 02/03/2023 at 4:30pm (fwd)
by Tiziano Vargiolu 01 Mar '23

01 Mar '23

****************************** WHEN? Thursday 2 March 2023 at 4:30pm WHERE? Room: 2BC60 - TORRE ARCHIMEDE, via Trieste 63, 35121 Padova (only in presence) WHO? Prof. Kostas Kardaras (LSE London) WHAT? Seminar on "Portfolio choice under taxation and time constraints" Abstract: We consider the problem of choosing an investment strategy that will maximise utility over distributions, under capital gains tax and constraints on the expected liquidation date. We show that the problem can be decomposed in two separate ones. The first involves choosing an optimal target distribution, while the second involves optimally realising this distribution via an investment strategy and stopping time. For the latter step, a variant of the Azema-Yor solution to the Skorokhod embedding problem is utilised, and its description is given very precisely in terms of solutions to algebraic equations.

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