Without introducing either debt constraints or transversality conditions to avoid the possibility of Ponzi schemes, we show the existence of equilibrium in an infinite horizon incomplete markets economy with a collateral structure.

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International audienceBy introducing repo markets we understand how agents need to borrow issued securities before shorting them: (re)-hypothecation is at the heart of shorting. Non-negative amounts of securities in the box of an agent (amounts borrowed or owned but not lent on) can be sold, and recursive use of securities as collateral allows agents to leverage their positions. A binding box constraint induces a liquidity premium: the repo rate becomes special and the security price higher than expected discounted cash-flows. Existence of equilibrium is guaranteed under limited re-hypothecation, a situation secured by (current or proposed) institutional arrangements

We study an economy where there are two types of assets. Consumers' promises are the primitive defaultable assets secured by collateral chosen by the consumers themselves. These personalized assets are purchased by financial intermediaries who finance these purchases by selling back derivatives to consumers. We show that non-arbitrage prices of primitive assets are strict submartingales, whereas non-arbitrage prices of derivatives are supermartingales. Next we establish existence of equilibrium, without imposing bounds on short-sales. The nonconvexity of the budget set is overcome by considering a continuum of agents.

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We study a two-period general equilibrium model with incomplete asset markets and default. We make collateral endogenous by allowing each seller of assets to fix the level of collateral. Sellers are required to provide collateral whose first-period value, per unit of asset, exceeds the asset price by an arbitrarily small amount. Moreover, borrowers are also required to be fully covered by the purchase, in the first period, of state-by-state default insurance. These insurance contracts are offered by lenders. The insurance cost or revenue is a linear charge and plays the role of a spread penalizing borrowers who will incur in default and benefiting lenders who will suffer default. Under these assumptions, equilibrium always exists. Copyright Blackwell Publishers, Inc. 2000.

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