An assets-liabilities dynamical model of banking system and systemic risk governance

We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the difference between assets and liabilities of the bank. A bank is solvent when its capital reserves are greater or equal to zero otherwise the bank is failed.The banking system dynamics is defined by an initial value problem for a system of stochastic differential equations whose independent variable is time and whose dependent variables are the assets and the liabilities of the banks.The banking system model presented generalizes those discussed in [4],[3] and describes a homogeneous population of banks. The main features of the model are a cooperation mechanism among banks and the possibility of the (direct) intervention of the monetary authority in the banking system dynamics. We call systemic risk or systemic event in a bounded time interval the fact that in that time interval at least a given fraction of the banks fails. The probability of systemic risk in a bounded time interval is evaluated using statistical simulation. The systemic risk governance pursues the goal of keeping the probability of systemic risk in a bounded time interval between two given thresholds.The monetary authority is responsible for the systemic risk governance.The governance consists in the choice of the assets and of the liabilities of a kind of "ideal bank" as functions of time and in the choice of the rules that regulate the cooperation mechanism among banks.These rules are obtained solving an optimal control problem for the pseudo mean field approximation of the banking system model. The governance induces the banks of the system to behave like the "ideal bank". Shocks acting on the assets or on the liabilities of the banks are simulated.