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1 results

  • LARGE-LOSS BEHAVIOR OF CONDITIONAL MEAN RISK SHARING

  • Michel Denuit, Christian Y. Robert
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 50 / Issue 3 / September 2020
    Published online by Cambridge University Press:
    13 July 2020, pp. 1093-1122
    Print publication:
    September 2020

  • We consider the conditional mean risk allocation for an insurance pool, as defined by Denuit and Dhaene (2012). Precisely, we study the asymptotic behavior of the respective relative contributions of the participants as the total loss of the pool tends to infinity. The numerical illustration in Denuit (2019) suggests that the application of the conditional mean risk sharing rule may produce a linear sharing in the tail of the total loss distribution. This paper studies the validity of this empirical finding in the class of compound Panjer–Katz sums consisting of compound Binomial, compound Poisson, and compound Negative Binomial sums with either Gamma or Pareto severities. It is demonstrated that such a behavior does not hold in general since one term may dominate the other ones conditional of large total loss.