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Law invariant risk measures and information divergences

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  • Lacker Daniel

    (Columbia University, Department of Industrial Engineering & Operations Research,New York, SUA)

Abstract

Aone-to-one correspondence is drawnbetween lawinvariant risk measures and divergences,which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy and convex f -divergences. Several properties of divergence and their duality with law invariant risk measures are characterized, such as joint semicontinuity and convexity, and we notably relate their chain rules or additivity properties with certain notions of time consistency for dynamic law risk measures known as acceptance and rejection consistency. The examples of shortfall risk measures and optimized certainty equivalents are discussed in detail.

Suggested Citation

  • Lacker Daniel, 2018. "Law invariant risk measures and information divergences," Dependence Modeling, De Gruyter, vol. 6(1), pages 228-258, November.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:228-258:n:14
    DOI: 10.1515/demo-2018-0014
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    References listed on IDEAS

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