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An Ambiguity Measure under EUUP and Its Application to a Portfolio Problem

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Document pages: 19 pages

Abstract: This paper derives a measure that quantifies the degree of ambiguity under expected utility with uncertain probability (EUUP) by [1]. Here, ambiguity means a situation in which the first-order probabilities, i.e., the probabilities of the states of nature, are not given uniquely, but as random variables. Because EUUP can completely distinguish attitudes toward both risk and ambiguity from beliefs and risk from ambiguity, the derived ambiguity measure is independent of risk and attitudes toward both risk and ambiguity. We show that the degree of ambiguity can be measured by the variance of the first-order probabilities. Although [2] also derives an ambiguity measure based on the variance of the first-order probabilities, our measure is more flexible, and it discriminates between ambiguity in favorable outcomes and in unfavorable ones. Based on the measure, we also discuss effects of ambiguity on a problem of portfolio selection through comparative statics.

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