article · Mathematics
A generalised mathematical model captures the complex dynamics of financial systems using three interconnected variables: the interest rate, investment demand, and the price index. The formulation builds upon existing financial frameworks by integrating two distinct time delays. One delay accounts for lags in price adjustment, while the second reflects delayed feedback influencing investment demand. A newly defined threshold parameter serves to determine the existence and characteristics of system equilibria. Mathematical analysis explores the system stability and identifies conditions under which Hopf bifurcations occur, marking transitions in dynamic behaviour. In addition, sensitivity analysis and numerical simulations demonstrate how variations in specific model parameters alter overall system stability and confirm theoretical findings.
Financial systems often react to market changes with significant delays, which can lead to volatility or sudden shifts in stability. By mathematically mapping how delayed price adjustments and feedback on investment demand interact with interest rates, this model provides a clearer understanding of how complex economic fluctuations and tipping points emerge in connected financial markets.
The abstract describes a theoretical mathematical framework supported by numerical simulations, representing early-stage research. While financial analysts, central banks, or risk management software developers could potentially use such modelling to study market instability and delayed market responses, the abstract does not indicate an explicit application pathway or direct testing in commercial software or policy tools.
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This paper develops a new generalized model to describe the complex dynamical behavior of a financial system through three state variables, namely the interest rate, investment demand and price index. The proposed model extends and improves numerous financial models available in the literature by incorporating two time delays. The first delay accounts for the time lag in price adjustment, whereas the second captures the delayed feedback effect on investment demand. For the first time in the context of financial systems, a novel threshold parameter is introduced to characterize the existence of equilibria. The dynamical properties of the proposed model, including the stability and occurrence of a Hopf bifurcation, are rigorously analyzed. Furthermore, sensitivity analysis and numerical simulations are conducted to investigate the influence of model parameters on the dynamics of the financial system and to illustrate the analytical results.
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DOI: 10.3390/math14162903
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