Provisions for bank deposit withdrawals and portfolio selection

The primary economic function of a bank is to redirect funds from savers to borrowers in an efficient manner, while increasing the value of the bank’s asset holdings in absolute terms. Within the regulatory framework of the Basel III accord, banks are required to maintain minimum liquidity to guard against withdrawals/liquidity risks. In this paper, we analyze a continuous-time mean-variance portfolio selection for a bank with stochastic withdrawal provisioning by relating the reserves as a proxy for the assets held by the bank. We then formulate an optimal investment portfolio selection for a banker by constructing a special Riccati equation as a continuous solution to the Hamilton–Jacobi–Bellman (HJB) equation under mean-variance paradigm. We obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of the reserve, depository, and intrinsic risk that are associated with the reserve process.