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New characterizations of increasing risk. (English) Zbl 1395.91102

Summary: I present alternative constructions of gambles with greater risk. M. Rothschild and J. E. Stiglitz [“Increasing risk: I. A definition”, J. Econom. Theory 2, 225–24 (1970)] demonstrate that gamble \(Y\) has greater risk than \(X\) when \(Y\) is equal in distribution to \(X + Z\), where \(Z\) is noise. Gambles called positive-upper-conditional-mean errors are introduced, and I show that \(Y\) has greater risk than \(X\) when \(Z\) is a PUCME and is not noise. Simple examples demonstrate that the set of PUCMEs is strictly greater than the set of gambles that are noise.

MSC:

91B06 Decision theory
91B16 Utility theory
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References:

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