ABSTRACT

N(0) = 0, N(t) = ξ1 + . . . + ξt, t = 1, 2, . . . ,

where (ξi)i=1,2,... is a sequence of independent Bernoulli random variables such that

P ({ω : ξi = 1}) = q and P ({ω : ξi = 0}) = 1− q .

Sequence of independent identically distributed random variables (Xi)i=1,2,... with values in the set of all natural numbers N, represents the amounts of claims. Denote

fn = P ({ω : Xi = n}) , f˜(z) =

fn z n , and μ = E(Xi)

the distribution, the generating function, and the expectation of (Xi)i=1,2,..., respectively.