Suppose that no arbitrage exists and that for some i. Then the economy E is complete if and only if there exists a unique equivalent martingale measure for the ‘unit’ A(i). Proof: Observe that in...

Suppose that no arbitrage exists and that


for some i. Then the economy E is complete if and only if there exists a unique equivalent martingale measure for the ‘unit’ A(i).

Proof: Observe that in the proof of Theorem 1.20 we established a one-to-one correspondence between pricing kernels and equivalent martingale measures. The result now follows from which establishes the equivalence of completeness to the existence of a unique pricing kernel. - Our final result, concerning the pricing of a derivative, is left as an exercise for the reader.