Endogenous collateral

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.