Suppose that the economy E is arbitrage-free and let X be an attainable contingent claim, i.e. a derivative which can be replicated with other assets. Then the fair value of X is given by   where φ...

Suppose that the economy E is arbitrage-free and let X be an attainable contingent claim, i.e. a derivative which can be replicated with other assets. Then the fair value of X is given by

where φ solves

Furthermore, if Z is some pricing kernel for the economy then X0 can also be represented as