The Optimal Design of Insurance Schemes for Preventing Liquidity Runs

Abstract

We analyze the optimal deposit insurance scheme that can prevent a liquidity run. We obtain a simple characterization of the optimal scheme. Based on this characterization, we examine how the insurance depends on the size of the investment. When comparing agents who are partially insured we show that on a per-dollar basis a larger investor should receive better insurance. However, the relation between size of investment and level of insurance need not be monotone as the largest investor is never fully insured.