On the Non-Optimality of a Diamond-Dybvig Contract in the Goldstein-Pauzner Environment

I show, under intuitive conditions on the risk-averse utility function, the nonoptimality of the Diamond and Dybvig (1983) contract in the Goldstein and Pauzner (2005) environment. If marginal utility at zero is low enough, then Goldstein and Pauzner (2005)’s claim about the optimality of the Diamond and Dybvig (1983) contract is true. When it is not, the optimal contract insures the patient depositor against a project default. The contract may exhibit risk-sharing with the impatient depositor. Unlike when Goldstein and Pauzner (2005)’s claim is correct, relative risk aversion greater than 1 does not necessarily make the optimal bank contract run-prone. I present a condition under which it is.