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On Stop-Loss Order and the Distortion Pricing Principle

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  • Hürlimann, Werner

Abstract

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.

Suggested Citation

  • Hürlimann, Werner, 1998. "On Stop-Loss Order and the Distortion Pricing Principle," ASTIN Bulletin, Cambridge University Press, vol. 28(1), pages 119-134, May.
    • Handle: RePEc:cup:astinb:v:28:y:1998:i:01:p:119-134_01
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    Cited by:

    1. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    2. Jianfa Cong & Ken Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.
    3. Jianfa Cong & Ken Seng Tan, 2016. "Optimal VaR-based risk management with reinsurance," Annals of Operations Research, Springer, vol. 237(1), pages 177-202, February.

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