A Study Of The Capital Adequacy Regulation Policy Based On The Maximization Of The Utility Of Terminal Wealth

As is well known, experts and scholars generally think that the government should implement counter-cyclical capital adequacy regulation policy according to the pro-cyclical commercial bank credit.Taking into account that banks can transfer around their capital in and out of the regulation depending on the severity of the regulation, however, we present a new conclusion that the capital adequacy regulation policy is pro-cyclical through depth analysis of the systematic risk of financial markets. This conclusion is not only the improvement and extension of the current counter-cyclical capital regulation policy, but also provides a new regulatory perspective for the practitioners of financial regulations.First of all, we model the behavior of the agents(banks, investors, government) in the financial market. In order to show the ability of banks to transfer capital, we regard banks as the investors of their equity capital, and then construct the banks’investment decision model based on the maximization of the utility of terminal wealth. We also construct the corresponding model of the utility of terminal wealth for investors and government.Secondly, we arrive at the solution of the models of the utility of terminal wealth by solving the HJB equation and then using the Legendre transform and the method of separation of variables. Then we obtain the explicit solution to the problem for CRRA utility function.Finally, we derive the optimal capital adequacy regulation policy through depth analysis of the explicit solution of models of the agents’ behavior. Furthermore, this paper analyzes and shows that the regulatory policy is pro-cyclical. Meanwhile, we have a brief analysis on the robustness of the regulatory policy.