Abstract
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.
Highlights
We introduce here the mathematical modelling framework adopted throughout the paper to model a dynamics of liquidity on a time evolving network that mimics a stylized financial market, following hints and research perspectives that arose in [1,2]
The kinetic theory of active particles (KTAP) provides mathematical tools to transfer into a mathematical model the collective dynamics of large systems of interacting living entities, which perfectly fit the peculiar phenomenology of financial markets
We study the dynamics in the liquidity profile of a financial system, arising when individuals interact through financial transaction on the market, by resorting to statistical methods for complex systems modelling the dynamics of the liquidity risk profile of a stylized financial system, artificially experimenting with liquidity management in the banking system
Summary
We introduce here the mathematical modelling framework adopted throughout the paper to model a dynamics of liquidity on a time evolving network that mimics a stylized financial market, following hints and research perspectives that arose in [1,2]. The kinetic theory of active particles (KTAP) provides mathematical tools to transfer into a mathematical model the collective dynamics of large systems of interacting living entities, which perfectly fit the peculiar phenomenology of financial markets. The paper proceeds as follows—Section 2 provides a concise phenomenological description of the process under consideration, characterizing the dynamics of liquidity on a time evolving network; Section 3 provides a description of the class of dynamical systems under consideration and the derivation of the specific mathematical model that describes the phenomenology; Section 4 is devoted to simulations in two case studies and the related interpretations of outcomes; Section 5 looks ahead to research perspectives. A short appendix devoted to some analytical derivations of the necessary conditions for equilibrium configurations of high quality liquid assets on time evolving networks closes the paper
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