Self-similar processes in collective risk theory
Conditions are given for an insurance risk process to converge weakly to a long-range dependent process, in particular fractional Brownian motion. Convergence of the associated ruin probabilities is discussed and various estimates of the ruin probabilities for fractional Brownian motion are given. The occurrence of long-range dependence in insurance risk is motivated by an example with alternating periods of safe and risky conditions, along the lines of \textit{D. Heath}, \textit{S. Resnick} and \textit{G. Samorodnitsky} [Ann. Appl. Probab. 9, No. 2, 352-375 (1999)].
scientific article; zbMATH DE number 1247733