The Fundamental Theorem of Asset Pricing

We saw in the previous chapter that the existence of a probability measure Q ~ P under which the (discounted) stock price process is a martingale is sufficient to ensure that the market model is viable; that is, it contains no arbitrage opportunities. We now address the converse: whether for every viable model one can construct an equivalent martingale measure for S, so that the price of a contingent claim can be found as an expectation relative to Q.