Sensitivity analysis of risk tolerance

For a risk-averse decision maker with exponential utility facing a decision between two investments X and Y, there may exist more than one critical value of risk tolerance for which the decision is reversed from one investment to the other. Our main result establishes that if Y is preferred to X by all risk-seeking decision makers, then there is at most one such critical value. We extend this result to linear plus exponential utility functions. The results reduce the input required from a decision maker.