Noncomputability, unpredictability, and financial markets

One of the most significant achievements from theoretical computer science was to show that there are non-computable problems, which cannot be solved through algorithms. Although the formulation of such problems is mathematical, they often can be interpreted as problems derived from other fields, like physics or computer science. However no noncomputable problem with economical or financial inspiration has been presented before. Here we study the problem of valuation: given some adequate data, find the value of an asset. Valuation is modeled mathematically by the discounted cash flow operator. We show, using surprisingly simple arguments, that this operator is not computable. Since, theoretically, financial markets should trade assets based on their fair value, our result suggests that unpredictability of such markets may partially stem from inherent non-computable behavior. A discussion of this result is also included.