Non-computability, unpredictability, and financial markets

• Autor(a) principal: Graça, Daniel
• Data de Publicação: 2012
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.1/1060

One of the most significant achievements from theoretical computer science was to show that there are non-computable problems, which can- not be solved through algorithms. Although the formulation of such prob- lems is mathematical, they often can be interpreted as problems derived from other elds, like physics or computer science. However no non- computable problem with economical or financial inspiration has been presented before.1 Here we study the problem of valuation: given some adequate data, find the value of an asset. Valuation is modeled mathemat- ically by the discounted cash ow operator. We show, using surprisingly simple arguments, that this operator is not computable. Since, theoreti- cally, 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.