Asset Pricing and Valuation under the Real-World Probability Measure

In general it is not a priori clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral probability measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I clarify the economic conditions under which the aforementioned problems evaporate and the discounted price processes in the financial market are martingales under the real-world probability measure. It turns out that risk-neutral valuation becomes superfluous if and only if the financial market is complete and efficient. This leads to a simple real-world valuation formula in a model-independent framework, where the number of assets as well as the lifetime of the market can be finite or infinite.