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The moments of ruin time in the classical risk model with discrete claim size distribution. (English) Zbl 0957.62089
The authors consider a classical ruin model with discrete claim sizes $$W_i$$, constant claim intensity $$c$$ and constant premium rate $$\lambda$$. Exact simple solutions are provided for the moments $$k$$ of ruin time for the case where the initial reserve $$u=0$$. Also, for the case of $$u$$ natural, an analytic expression is derived. The calculation involves recursive calculations in terms of $$k$$ and $$u$$ which can be rolled out into finite sums over $$r,\dots,u$$. The calculations are built on a generalized Appell structure of polynomials. Both cases $$c>$$ and $$c\leq\lambda E[W_i]$$ are treated.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010)
##### Keywords:
ruin theory; risk theory
Full Text:
##### References:
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