An incentive problem in the dynamic theory of banking

Abstract 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 framework, 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.

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