THE EXISTENCE OF SECURITY MARKET EQUILIBRIUM WITH A NONATOMIC STATE-SPACE

We consider a finite horizon economy with incomplete markets and, at e ach period, a non-atomic continuum of states of nature, We combine bac kward recursion methods with a reformulation of the problem in terms o f first-order conditions to establish the existence of a Radner equili brium. One of our hypotheses, not required in the case of a finite num ber of states, says that in any date and state the position reached af ter any possible previous asset trades, but before spot trades, consti tutes a feasible consumption. An example shows that this hypothesis ca nnot be dispensed with (even in the case of countable many states).