We introduce a new equilibrium concept and study its efficiency and asset pricing implications for the environment analyzed by Kehoe and Levine (1993) and Kocherlakota (1996). Our equilibrium concept has complete markets and endogenous solvency constraints. These solvency constraints prevent default at the cost of reducing risk sharing. We show versions of the welfare theorems. We characterize the preferences and endowments that lead to equilibria with incomplete risk sharing. We compare the resulting pricing kernel with the one for economies without participation constraints: interest rates are lower and risk premia depend on the covariance of the idiosyncratic and aggregate shocks. Additionally, we show that asset prices depend only on the valuation of agents with substantial idiosyncratic risk.