Entropy and the value of information for investors

摘要

Consider a person or say agent who has to take decision on investments who needs information about the investment. When the agent has to rank information the basis for the same has to be decided. Ranking of information value depend up on agents prior information, the preferences and wealth of the agent and the decision problem to which the information is applied. The agent may have some initial prior on a set of pay-off related states of nature. He receives signals and based on this his beliefs are updated. The problem is regarding whether one information structure more useful information than another. This was first discussed by Blackwell (Ref.1 ). The summary of Blackwell's approach is that when a later information is appealing than the former, it means that the former signal is less informative or the same as later but with noise. However Blackwell's theory assumes that the agent has a preference for information structure over the other and thus ordering of information may not be feasible in this approach. In this paper decision-theoretic principles are used for make the Blackwell's approach complete restricting the attention to no-arbitrage investment decisions. Fixing a prior over the states, one information structure investment dominates another if, over the allowed class of problems and preferences, whenever the first one is rejected at some price, so is the case with the second. (33 refs.)