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 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 ? ? -stably distributed when the net profit of a policy belongs to the domain of attraction of an ? ? -stable distribution with index ? ? (0<??2) ( 0 < ? ? 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.
canonical measure heavy-tailed distribution insurance risk process nonhomogeneous poisson process infinite divisible distribution ? ? -stable distribution ? ? ? ? ?