Price dynamics in financial markets: a kinetic approach

The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and discussed

Local energy methods for free boundary problem

La tesi riguarda alcune tecniche locali per lo studio di problemi di frontiera libera per una classe di equazioni ellittiche e paraboliche

Microscopic and Kinetic Models in Financial Markets

The aim of this PHD thesis is to rewiew some of the more influential models of multi-agent interactive systems in financial markets and to present a new kinetic approach to the description of etherogeneous systems, where different populations of agents are involved and interact each others. In the first chapter, we present the Levy-Levy-Solomon model and The Lux-Marchesi model as mi- crospic models. In the second chapter staring from the microsopic description we derive kinetics model for both Levy-Levy solomon and Lux-Marchesi models, furthermore through the introduction ok Fokker-Plank appoximation models, we are able yo illustrate some analitycal results and numerical simulations. In the third chapter we present a more realistic whic generalize the works of chapter two. For such model, starting from a mesoscopic decription an hydrodynamic model is derived and analytical and numerical results are provided. We leave as appendix A and B full details of some technical proofs of the second chapter, in order to let it more readable. Appendix C contains a pub- blication in the Esaim Proceedings where I’m co-author. It was the results of the CEMRACS summer school held in Marseille in the August 2010. Here a spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem is investigated and compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme

HYBRID MODEL FOR THE COUPLING OF AN ASYMPTOTIC PRESERVING SCHEME WITH THE ASYMPTOTIC LIMIT MODEL: THE ONE DIMENSIONAL CASE.

International audienceIn this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, ellip-tic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this paper is well suited for the simulation of a plasma in the presence of a magnetic field, whose intensity may vary considerably within the simulation domain