Random deposits, technical insolvency and deposit insurance pricing

Economists have proposed various ways to induce depository institutions to internalize the expected losses on their excessive risk-taking behavior. We develop a model that offers two distinctive advantages. First, it considers the liquidity problems associated with demand deposits, which means that the closure of a bank may be triggered not only in the case of the inability to pay all debts, but also in the case of technical insolvency. Second, the model allows the exercise price of deposit insurance option to be different with the triggered price when the insurer liquidates a bank. The actuarially fair deposit insurance premium consists the expected loss from the bank being insolvent and the expected loss from being solvent but illiquid.