An Optimal Investment Strategy and Multiperiod Deposit Insurance Pricing Model for Commercial Banks

Abstract

We employ the method of stochastic optimal control to derive the optimal investment strategy for maximizing an expected exponential utility of a commercial bank’s capital at some future date $T>\mathrm{0}$. In addition, we derive a multiperiod deposit insurance (DI) pricing model that incorporates the explicit solution of the optimal control problem and an asset value reset rule comparable to the typical practice of insolvency resolution by insuring agencies. By way of numerical simulations, we study the effects of changes in the DI coverage horizon, the risk associated with the asset portfolio of the bank, and the bank’s initial leverage level (deposit-to-asset ratio) on the DI premium while the optimal investment strategy is followed.