Buongiorno a tutt*,
ho il piacere di annunciare il prossimo webinar del ciclo di seminari online
promosso dal Gruppo UMI PRISMA (http://www.umi-prisma.polito.it/index.html)
*Lunedì 3 aprile 2023*
ore 16-17 LUCIANO CAMPI
Title: Correlated equilibria and mean field games
Abstract: In the context of mean field games (MFGs), we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. The latter is a generalization of Nash equilibrium for stochastic games. Our notion of solution can be justified in two ways for MFGs in discrete time and finite state space: correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying $N$-player games, and approximate $N$-player correlated equilibria can be constructed starting from a correlated solution to the mean field game. Moreover, those results can be extended to progressive deviations, possibly depending on the whole history of the state and the flow of measures. In this talk we will focus especially on a further extension to continuous time MFGs through the notion of coarse correlated equilibrium. This talk is based on joint works with O. Bonesini, F. Cannerozzi and M. Fischer.
ore 17-18 GIORGIA CALLEGARO
Title: McKean–Vlasov Game of Commodity Production, Consumption and Trading
Abstract: We propose a model where a producer and a consumer can affect the price dynamics of some commodity controlling drift and volatility of, respectively, the production rate and the consumption rate. We assume that the producer has a short position in a forward contract on λ units of the underlying at a fixed price F, while the consumer has the corresponding long position. Moreover, both players are risk-averse with respect to their financial position and their risk aversions are modelled through an integrated-variance penalization. We study the impact of risk aversion on the interaction between the producer and the consumer as well as on the derivative price. In mathematical terms, we are dealing with a two-player linear-quadratic McKean–Vlasov stochastic differential game. Using methods based on the martingale optimality principle and BSDEs, we find a Nash equilibrium and characterize the corresponding strategies and payoffs in semi-explicit form. Furthermore, we compute the two indifference prices (one for the producer and one for the consumer) induced by that equilibrium and we determine the quantity λ such that the players agree on the price. Finally, we illustrate our results with some numerics. In particular, we focus on how the risk aversions and the volatility control costs of the players affect the derivative price. Joint work with R. Aid, O. Bonesini and L. Campi.
Il link per partecipare è il seguente
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Cari saluti,
Claudia Ceci
Claudia Ceci
Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza (MEMOTEF)
Università di Roma La Sapienza Via Del Castro Laurenziano 9 Roma 00161 Italy
Email: claudia.ceci@uniroma1.it