P. Jordanova, Milan Stehlik,
"On multivariate modifications of Cramer Lundberg risk model with constant intensities"
, in Stochastic Analysis and Applications, 2018
On multivariate modifications of Cramer Lundberg risk model with constant intensities
Sprache des Titels:
The paper considers very general multivariate modifications of Cramer?
Lundberg risk model. The claims can be of different types and can
arrive in groups. The groups arrival processes have constant intensities.
The counting groups processes are dependent multivariate compound
Poisson processes of Type I. We allow empty groups and show that
in that case we can find stochastically equivalent Cramer?Lundberg
model with non-empty groups. The investigated model generalizes the
risk model with common shocks, the Poisson risk process of order k, the
Poisson negative binomial, the Polya-Aeppli, the Polya-Aeppli of order k
amongothers.All of them with one or more types of policies. The numerical
characteristics, Cramer?Lundberg approximations, and probabilities
of ruin are derived. During the paper, we show that the theory of these
risk models intrinsically relates to the special types of integro differential equations. The probability solutions to such differential equations provide new insights, typically overseen from the standard point of view.