### Abstract

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized version, respectively, of) the popular maxmin expected utility theory of Gilboa and Schmeidler [12] whenever the negative certainty equivalents are translation invariant. In addition, we derive the dual conjugate function for entropy coherent and entropy convex measures of risk, and prove their distribution invariant representation.
Keywords: Robust preferences; Convex risk measures; Exponential utility; Relative entropy; Translation invariance; Convexity.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 34 |

Publication status | Published - 2010 |

### Publication series

Name | Report Eurandom |
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Volume | 2010020 |

ISSN (Print) | 1389-2355 |

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## Cite this

Laeven, R., & Stadje, M. A. (2010).

*Entropy coherent and entropy convex measures of risk*. (Report Eurandom; Vol. 2010020). Eurandom.