Mean-Risk Decision Analysis Under Partial Information

Abstract

In many practical economic decision problems, e.g. project appraisal, actual probability information about the states of nature lies somewhere between risk and ignorance. There is empirical evidence that, in such cases of partial information, decision-makers use a sort of mean-risk decision rule. In this paper, the classical mean-risk decision principle is generalized to the case of decisions under partial information. First, a theory of pure risk under partial information is developed: only potential losses are considered. Then, an outline of a theory of speculative risk is given: besides potential losses also potential gains are allowed. Based on this risk theory, a decision principle is proposed which is a generalization of classical mean-risk decision principles. Thereby, the mean is substituted by the payoff in the state which the decision-maker believes to obtain most likely. It is shown that this decision principle is suitable to solve the well-known Ellsberg paradox.