, 17:139

How retention levels influence the variability of the total risk under reinsurance

Original Paper

DOI: 10.1007/s11750-009-0085-4

Cite this article as:
Escudero, L.F. & Ortega, EM. TOP (2009) 17: 139. doi:10.1007/s11750-009-0085-4


Recently, Escudero and Ortega (Insur. Math. Econ. 43:255–262, 2008) have considered an extension of the largest claims reinsurance with arbitrary random retention levels. They have analyzed the effect of some dependencies on the Laplace transform of the retained total claim amount. In this note, we study how dependencies influence the variability of the retained and the reinsured total claim amount, under excess-loss and stop-loss reinsurance policies, with stochastic retention levels. Stochastic directional convexity properties, variability orderings, and bounds for the retained and the reinsured total risk are given. Some examples on the calculation of bounds for stop-loss premiums (i.e., the expected value of the reinsured total risk under this treaty) and for net premiums for the cedent company under excess-loss, and complementary results on convex comparisons of discounted values of benefits for the insurer from a portfolio with risks having random policy limits (deductibles) are derived.


Excess-loss reinsurance Stop-loss reinsurance Stochastic directional convexity Directionally convex functions Increasing convex order 

Mathematics Subject Classification (2000)

60E15 62P05 

Copyright information

© Sociedad de Estadística e Investigación Operativa 2009

Authors and Affiliations

  1. 1.Dpto. Estadística e Investigación OperativaUniversidad Rey Juan CarlosMóstolesSpain
  2. 2.Centro de Investigación OperativaUniversidad Miguel HernándezOrihuelaSpain

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