  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.
