Properties of a renewal process approximation for a spin market model

TL;DR

This paper explores how phase transitions in a spin market model depend on interaction strength, revealing robust periodic behavior unaffected by temperature or market size.

Contribution

It introduces a renewal process approximation to analyze phase transitions in a stylized spin market model, highlighting the robustness of periodicity.

Findings

Periodic dynamics depend on coupling constant

Periodicity is robust to temperature changes

Market size does not affect the periodic behavior

Abstract

In this short note we investigate the natur of the phase transitions in a spin market model as a function of the interaction strength between local and global effects. We find that the stochastic dynamics of this stylized market model exhibit a periodicity whose dependence on the coupling constant in the Ising-like Hamiltonian is robust to changes in the temperature and the size of the market.