Bank capital regulation with random audits

We consider a model of optimal bank closure rules (cum capital replenishment by banks), with Poisson-distributed audits of the bank's asset value by the regulator, with the goal of eliminating (ameliorating) the incentives of levered bank shareholders/managers to take excessive risks in their choice of underlying assets. The roles of (tax or other) subsidies on deposit interest payments by the bank, and of the auditing frequency are examined.