A Mathematical Modeling Method And Research On Banking Bubbles

The existence of stock banking bubbles may affect the development of real economy,the bubbles burst could lead to financial crisis.Therefore,it is a great concern to research on mathematical molding of banking bubbles.This paper constructs a dynamic stochastic general equilibrium model for banking bubbles to describe the dynamical path of the stock bubbles in bank sector and the influence of the bubbles to macro-economy.The model contains three sectors: households,firms and banks.The purpose of households is to maximize their consumption under budget constraint,the purpose of firms is to minimize their cost under production function,and the purpose of banks is to maximize their stock value under borrowing constraint.We constructs the model above,then gives out the difference equations of the model using dynamic programming and the Bellman equation.Finally,calibration and numerical simulations are used to solve the model.According to the results,the model in the paper can reflect the real economy.If the households have a lot of confidence in the banks,it can lead to the change of the borrowing constraint and thus lead to the existence of bank bubbles.The existence of banking bubbles can have positive effects on the real economy.The amount of bank capital,output,salary and consumption will rise when banking bubbles exist.If the confidence of the households change,the bubbles may burst.After bubbles burst,the amount of bank capital,output,salary and consumption will decrease and these values will not easily rise to the former level in a long term.Proper amount of capital requirements can help to avoid the formation of the banking bubbles.Credit policy can lessen the loss of economic strength immediately after bubbles bursting.