Entropy and the value of information for investors

Antonio Cabrales (1) , Olivier Gossner (2, 3, 4) , Roberto Serrano (5, 6)

1 Departamento de Economía
2 PSE - Paris-Jourdan Sciences Economiques
3 PSE - Paris School of Economics
4 LSE - London School of Economics and Political Science
5 Department of Economics
6 Institute IMDEA Software [Madrid]

Consider any investor who fears ruin when facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure $\alpha$ is more informative than information structure $\beta$ if, whenever he is willing to buy $\beta$ at some price, he is also willing to buy $\alpha$ at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.

Mots clés: Informativeness; Information structures; Entropy; Decision under uncertainty; Investment; Blackwell ordering

Domaines: Economies et finances

Antonio Cabrales, Olivier Gossner, Roberto Serrano. Entropy and the value of information for investors. 2011. ⟨halshs-00648884⟩