Complete markets: security market equlibrium same as contingent commodity equilibrium?
You seem to be looking for information on the Radner equilibrium.


  Radner equilibrium is an economic concept defined by economist Roy Radner in the context of general equilibrium. The concept is an extension of the Arrow–Debreu equilibrium and the base for the first consistent incomplete markets framework.


Further reading: 
Jstor: Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets 
Handbook of Mathematical Economics: Chapter 20