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 tt, the distribution of the risk process is investigated. By using the theory of the canonical measure, we show that the risk process is asymptotically αα-stably distributed when the net profit of a policy belongs to the domain of attraction of an αα-stable distribution with index αα(0<α≤2)(0<α≤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.