Semi-parametric approach for approximating the ruin probability of classical risk models with large claims

Abstract

In this work, we consider the problem of the approximation of the ruin probability of a classical risk model with large claims using the strong stability method, when the claim distribution is unknown. Since claims are positive variables, we propose a semi-parametric approach to estimate the loss function associated with this distribution. First, a start parametric distribution (Champernowne generalized distribution) is used to transform the initial data. We then apply to the sample resulting from the first step the asymmetric Beta kernel estimator to avoid the problem of boundary effects. Two normalized versions: local (micro-Beta) and global (macro-Beta) are used to avoid the problem of inconsistency of this estimator at boundaries. Simulation studies are performed to support the results. A comparative study between the stability bounds on the ruin probability obtained using the semi-parametric proposed approach and asymmetric non-parametric kernel estimates is carried out to show the performance and the efficiency of the former.

Keywords:

• Beta kernel
• Champernowne generalized distribution
• Kernel estimation
• Risk model
• Ruin probability
• Strong stability

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 34K20
• 91G70
• 62G07
• 62G32