Mathematical modeling and optimal control of the impact of rumors on the banking crisis

The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.