This thesis develops models for three problems of liquidity under asymmetric information. In the chapter "Disclosures, Rollover Risk, and Debt Runs" I build a model of dynamic debt runs without perfect information in order to understand the impact of asset opacity and disclosure policies on run likelihood and economic efficiency. I find that opacity is desirable with respect to both these metrics if and only if fundamentals are strong enough; and that a bank should commit to disclose truthfully any information it has unless the level of opacity is large. The model also uncovers rich interactions between debt dynamics, beliefs dynamics and equilibrium outcomes: short-term yields may remain low while risk builds up in the background, and therefore may not contain a warning sign of an upcoming crisis; and a disclosure regime might produce higher beliefs about collateral quality but nevertheless imply larger financing costs and thus lead to a bank failure. In the chapter "Short-term Bank Leverage and the Value of Liquid Reserves", we extend the modelling toolbox of the global games literature by providing a fully rational setup where liquid reserves are modeled explicitly. The banks' balance sheet decisions and the prices of all securities are endogenous in the model. A bank possesses two instruments to manage illiquidity risk: its funding policy and the size of its liquid asset holdings,modeled as government bonds. Higher short-term indebtness allows the bank to better capture the liquidity benefits priced into deposits but increases illiquidity risk. Holding more bonds makes the bank more robust to withdrawals but it reduces the bank's asset returns. The impact of an increase in bond supply on bank leverage depends on the general-equilibrium change in the cost of absorbing the supply. The model also illustrates how considering an endogenous leverage decision is key to predict the impact of the economic environment on the liquidity premium. In the chapter "Insider Trading under Penalties", we establish existence and uniqueness of equilibrium in a generalised one-period Kyle (1985)model where insider trades can be subject to a size-dependent penalty. The result is obtained by considering uniform instead of Gaussian noise and holds for virtually any penalty function. We apply this result to regulation issues. We show that the penalty functions maximising price informativeness for given noise traders' losses eliminate small rather than large trades. We generalise this result to cases where a budget constraint distorts the set of penalties available to the regulator.