A New Generalized Financial Model in the Presence of Price Change Delay and Delayed Feedback on Investment Demand

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.