New Frontiers in Applied Probability

نویسندگان

  • TOMASZ ROLSKI
  • AGATA TOMANEK
چکیده

Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We consider the cases when X is Poisson and when X is mixed Poisson. The problem is motivated by modeling loss reserves in nonlife insurance.

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تاریخ انتشار 2011