The limit behavior of a risk model based on entrance processes
We construct a new insurance risk model based on the entrance process by incorporating a constant force of interest and by allowing a policy to be claimed more than once during its validity term, and study the central limit theorem of the correlative risk process. For fixed t, the distribution of the risk process is investigated. By using the theory of the canonical measure, we show that the risk process is asymptotically alpha-stably distributed when the net profit of a policy belongs to the domain of attraction of an alpha-stable distribution with index alpha(0 < alpha <= 2). Finally, we consider a special case in which each policy is restricted to being claimed at most once and obtain the weak convergence results under two very explicit moment conditions: heavy-tailed distribution and finite second moment of claims. (C) 2008 Elsevier Ltd. All rights reserved.
canonical measure alpha-stable distribution heavy-tailed distribution insurance risk process nonhomogeneous poisson process infinite divisible distribution