Boltzmann games in heterogeneous consensus dynamics

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (12/12/2017 preprint arXiv:1712.03224)

We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leaders' population. Derivation of the corresponding Fokker-Planck model permits to investigate the asymptotic behaviour of the solution.

Particle based gPC methods for mean-field models of swarming with uncertainty

Jos√© Antonio Carrillo, Lorenzo Pareschi, Mattia Zanella (5/12/2017 preprint arXiv:1712.01677)

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the

Portfolio Optimization and Model Predictive Control: A Kinetic Approach

Torsten Trimborn, Lorenzo Pareschi, Martin Frank (9/11/2017 preprint

In this paper, we introduce a large system of interacting financial agents in which each agent is faced with the decision of how to allocate his capital between a risky stock or a risk-less bond. The investment decision of investors, derived through an optimization, drives the stock price. The model has been inspired by the econophysical Levy-Levy-Solomon model (Economics Letters, 45).

A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs

Shi Jin, Hanqing Lu, Lorenzo Pareschi (16/10/2017 preprint arXiv:1710.05722)

In this paper, we develop a stochastic Asymptotic-Preserving (sAP) scheme for the kinetic chemotaxis system with random inputs, which will converge to the modified Keller-Segel model with random inputs in the diffusive regime.