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We take advantage of the challenging comments to the modeling approach we proposed in [35] to look ahead at a number of applications of the methods to the alternative questions these comments raise. In turn, our effort results in a number of interesting and valuable research perspectives. The presentation goes along three main lines. In the first line, we summarize briefly the aims and results in [35]. In the second section we give a technical the issues raised and, finally, the focus moves to the above mentioned research perspectives.

A learning dynamics on network is introduced, characterized by binary and multiple nonlinear interactions among the individuals distributed in the different nodes. A particular topology of the network is considered by introducing a leader node which influences all the other “follower” nodes without being influenced in turn. Numerical simulations are provided, particularly focusing on the effect of the network structure and of the nonlinear interactions on the emerging behaviour of the system. It turns out that the leader node always exhibits an autonomous evolution, while the follower nodes may have a regression when the interactions with the leader node are switched off. There is instead a remarkable change in the final configurations of the follower nodes, even if only one of them is connected to the leader: indeed, due to the microscopic interactions among them, all the follower nodes feel a strong “leader effect”.

The complex interactions between human behaviors and social economic sciences is critically analyzed in this paper in view of possible applications of mathematical modeling as an attainable interdisciplinary approach to understand and simulate the aforementioned dynamics. The quest is developed along three steps: Firstly an overall analysis of social and economic sciences indicates the main requirements that a contribution of mathematical modeling should bring to these sciences; subsequently the focus moves to an overview of mathematical tools and to the selection of those which appear, according to the authors bias, appropriate to the modeling; finally, a survey of applications is presented looking ahead to research perspectives.

We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed.

In this paper we present a kinetic model with evolutive stochastic game-type interactions, analyzing the relationship between the level of political competition in a society and the degree of economic liberalization. The above issue regards the complex interactions between economy and institutional policies intended to introduce technological innovations in a society, where technological innovations are intended in a broad sense comprehending reforms critical to production [3]. A special focus is placed on the political replacement effect described in a macroscopic model by Acemoglu and Robinson (AR-model [1], henceforth), which can determine the phenomenon of innovation 'blocking', possibly leading to economic backwardness. One of the goals of our modelization is to obtain a mesoscopic dynamical model whose macroscopic outputs are qualitatively comparable with stylized facts of the AR-model and the comparison is settled in a number of case studies. A set of numerical solutions is presented showing the non monotonous relationship between economic liberalization and political competition in particular conditions, which can be considered as an emergent phenomenon of the analyzed complex socioeconomic interaction dynamics. Fil: Dolfin, M.. Universita Degli Studi Di Messina; Italia Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina Fil: Leonida, L.. University College London; Estados Unidos Fil: Maimone Ansaldo Patti, D.. Universita Degli Studi Di Messina; Italia

The kinetic theory approach is successfully used to model complex phenomena related to social systems, allowing to predict the dynamics and emergent behavior of large populations of agents. In particular, kinetic theory for active particles (KTAP) models are usually analyzed by numerically solving the underlying Boltzmann-type differential equations through ad-hoc implementations. In this paper, we present KAOS: a kinetic theory of active particles modeling and analysis software tool. To the best of our knowledge, KAOS represents the first attempt to design and implement a comprehensive tool that assists the user in all the steps of the modeling process in the framework of the kinetic theories, from the model definition to the representation of transient solutions. To show the KAOS features, we present a new model capturing the competition/cooperation dynamics of a socio-economic system with welfare dynamics, in different socio-political conditions