Forecasting efficient risk/return frontier for equity risk with a KTAP approach - A case study in milan stock exchange

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

A kinetic theory model of the dynamics of liquidity profiles on interbank networks

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures