Entropy and the value of information for investors

Consider an investor who fears ruin when facing investments that satisfy no-arbitrage. Before investing he can purchase information about the state of nature as an information structure. Given his prior, information structure α investment dominates information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α 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.