Simple market structures are incomplete

We study how risk is shared using simple assets, each of which pays on a specific subset of payoff-relevant variables. We show that a market composed of simple assets is incomplete – no matter how many or which assets exist– because it can never address the joint realizations of some distinct risks. We also show that this inability to refine trades generates spill overs between agents with different types of financial constraints. Agents of type i are exposed to uninsurable income risk unless there exists another type j who can condition on all variables affecting i’s income.