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On Stop-Loss Order and the Distortion Pricing Principle

Published online by Cambridge University Press:  29 August 2014

Werner Hürlimann
Werner Hürlimann*
Affiliation:
Winterthur
*
Mathematik KB L, “Winterthur”, Paulstr. 9, CH-8401 Winterthur, Switzerland
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Abstract

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A number of more or less well-known, but quite complex, characterizations of stop-loss order are reviewed and proved in an elementary way. Two recent proofs of the stop-loss order preserving property for the distortion pricing principle are invalidated through a simple counterexample. A new proof is presented. It is based on the important Hardy-Littlewood transform, which is known to characterize the stop-loss order by reduction to the usual stochastic order, and the dangerousness characterization of stop-loss order under a finite crossing condition. Finally, we complete and summarize the main properties of the distortion pricing principle.

Keywords

Pricing theorydistortion functionquantile functionstop-loss orderstochastic orderHardy-Littlewood transform

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 119 - 134
Copyright
Copyright © International Actuarial Association 1998

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