General equilibrium with asymmetric information and default penalties

We introduce a two-period general equilibrium model with uncertainty and incomplete financial markets, where default is allowed and agents face in case they do default an utility penalty, which is their own private information. In this setting, if agents have heterogeneous characteristics they will generally pay different returns on any given asset, and thus the same promise made by different agents is in fact not equivalent. If asset trading is anonymous, then the same price is paid for promises whose value can be in fact quite different, and very severe adverse selection problems may arise as consequence. We thus incorporate in the above model an alternative way to negotiate the financial assets, under which an equilibrium exists and the adverse selection problem is mitigated. Succinctly, consumers trade assets non-anonymously with a set of financial intermediaires not allowed to default