On a Characterization of Poisson law with applications to the extended risk model in non-life insurance

DOI: 10.5176/2251-1911_CMCGS18.36

Authors: J.-R. Pycke

Abstract: We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generaliza- tion of a characterization of Poisson law due to Renyi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions oc- curring in the extended collective model in non-life insurance.

Keywords: non-life insurance, extended collective model, moments and cumulants, quantitative methods