Insurance Modelling under Natural Catastrophe for Dependent Risks and Survival Probabilities

Abstract

We consider the application of probability to an insurance portfolio under a dependent setting for the claim sizes and claim interval times in a renewal risk model, where the time between two claim sizes determines the next claim size. An explicit solution for the probability of survival of the insurance companies is derived for claim inter interval times and Erlang(2) distributed claim sizes, using Laplace-Stieltjes transform. Numerical examples are given to illustrate the main results and survival probability of insurance companies is calculated by simulation using R software.