Finite time ruin probability and structural density properties in the presence of dependence in insurance risk model

ABSTRACT

In the present paper, we consider the classical compound Poisson risk model with dependence between claim sizes and claim inter-arrival time. We attempt to analyze the approximation of finite time ruin probability. The finite time ruin probabilities are plotted for fixed threshold value associated to the claim inter-arrival time and also for fixed dependence parameter in Nelsen (2006) copula separately. Additionally, a general form for joint density of the interclaim times and claim sizes is considered. With respect to the classical Gerber-Shiu's (1998) function, first some structural density properties of dependent collective risk model is obtained. Then the ladder height probability density function of claim sizes is computed and the dependency structure investigated for Erlang interclaim time. As the application, some dependent models of the interclaim times and claim sizes are studied.

KEYWORDS:

• Dependent claims
• Insurance company
• Laplace transform
• Risk model
• Ruin probability.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G32
• 62F99
• 62E20

Acknowledgment

The authors are deeply grateful to the referees for their important and valuable comments and suggestions that led to considerable improvements of this paper. The first author lovingly dedicate this paper to his wife for supporting in each step of the life.