This thesis consists of a series of essays on the theory of exchange under uncertainty. The first essay examines the welfare implications of futures markets in the context of complete markets for contingent claims. It is shown that in a C-good, S-state world the equilibrium allocations resulting from the operation of pre-state noncontingent futures markets and post-state spot markets may be Pareto optimal. This proposition turns on the fact that a futures contract can be interpreted as a security whose state-specific return is the post-state spot price. If the matrix of spot prices has rank S, then, with futures and spot markets, agents can achieve the same allocations over states as with complete markets for contingent claims.