Abstract
In order to help regulators to control credit risk contagion effectively when the financial crisis happens, this paper first proposes a new nonlinear SIS/R (Susceptible–Infected–Susceptible/Removed) model to describe the real dynamic of risk spreading, which is more reasonable compared with traditional epidemic models. We provide a comprehensive nonlinear analysis of monotonicity, threshold conditions, stability properties, and asymptotic convergence for the SIS/R model. Moreover, we formulate a time-varying optimal dual control problem considering the macro-prudential tools and the easy monetary policy. By applying Pontryagin’s minimum principle, we obtain the existence of a solution and its uniqueness for sufficient small regulatory deadlines. At last, the theoretical results are confirmed by numerical simulations. We show the effectiveness of the optimal dual regulatory strategy against the constant dual strategy and no control strategy. The sensitivity of the control cost to the model parameters is also shown.
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