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.

我们考虑了Denuit和Dhaene（2012）定义的有条件的平均风险分配。精确地，我们研究参与者各自相对贡献的渐近行为，因为池的总损失趋于无穷大。Denuit（2019）中的数字说明表明，条件平均风险分担规则的应用可能会在总损失分布的尾部产生线性分担。本文在由复合二项式，复合泊松和复合负二项式和（具有伽玛或帕累托严重性）的复合Panjer-Katz和类别中研究了这一经验发现的有效性。事实证明，这种行为通常不成立，因为一个条件可能会在总损失较大的情况下主导另一个条件。