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.