Abstracts

We build a multi-agent economic model as a dynamical system on a compact set, and show that the market instability is closely related to the leverage and borrowing capacity of the market participant. The economy under consideration can be a single domestic economy, or a global one which consists of multiple subeconomies. First, we divide an economy into finitely many aggregates called economic “agents,” and build a deterministic dynamical system of their wealth. We use well-known theories of dynamical systems to represent a financial crisis as the breakage of a financial equilibrium and subsequent propagation of negative shock on wealth. Secondly, we define an early warning system, the market instability indicator, as the spectral radius of the Jacobian matrix of the wealth dynamical system. We show that the size of the indicator is proportional to the instability level of the economic system, therefore monitoring the indicator would enable us to predict upcoming financial crises. Thirdly, using the market instability indicator we give a quantitative definition of financial instability contagion, and provide a thorough mathematical analysis on the mechanism of instability contagion. Lastly, we use macroeconomic data from a period containing recent financial crises to test the market instability indicator and instability contagion model, and discuss limitation in their application in real life, such as data availability and frequency. Our contribution is to provide a methodology to quantify and monitor the level of financial instability in sectors and stages of a structured global economic model and how it may propagate between its components.