In our earlier analysis of models with complete markets we have considered simple one- or two-period economies with a discrete number of states and commodities. We now consider complete contingent claims equilibrium in economies with an infinite number of dates. We describe how to price claims that have payoffs for all possible events and discuss the implications of perfect risk sharing for such economies.

We start with a complete contingent claims market in which all trading is done at time zero, before any events have occurred. The purpose is to illustrate an important property of contingent claims markets that are complete, namely that the resulting consumption path depends only on the current state and not on the history of the system. We examine an economy where there is aggregate uncertainty: the total endowment is stochastic and exogenous. In these types of economies, aggregate risk in output cannot be diversified away by the economy as a whole, but there are implications for optimal risk sharing that emerge from the contingent claims prices. Next we take the same economy, but now assume that trading is done sequentially over time, as we actually observe. We find remarkably that the consumption allocation chosen when all state-contingent trades are executed at time zero is identical to the consumption allocation under sequential trading.

We then turn to idiosyncratic risk – risk that is individual-specific. Under certain circumstances, agents can face idiosyncratic risk even though there is no aggregate risk.