An Incentive Problem in the Dynamic Theory of Banking

This paper develops a continuous-time model of liquidity provision by banks, in which customers can deposit and withdraw their funds strategically. The strategic withdrawal option introduces an incentive-compatibility problem that turns the problem of designing deposit contracts into a non-standard, non-convex optimal control problem. The paper develops a solution method for this problem and shows that, in this more general frame-work, the insights obtained from the traditional banking models change considerably, up to the point of liquidity provision becoming impossible. The continuous-time framework allows to discuss the problem elegantly and may help to make this part of the banking literature more operational in the sense of modern asset pricing theory.