We solve the general problem of optimal risk sharing among a nite number of agents with limited liability. We show that the optimal allocation is characterized by endogenously determined ranks assigned to the participating agents and a hierarchical structure of risk sharing, where all agents...

We develop a general model of decentralized exchange. Our model allows for any number of traders and traded assets, and any form of market decentralization, including trading environments determined by an arbitrary network structure. We study how the equilibrium allocation and liquidity depend...

We develop a two-period general equilibrium model of portfolio delegation with competitive, differentially skilled managers and convex compensation contracts. We show that convex incentives lead to significant equilibrium mispricing, but reduce price volatility. In particular, price...