Abstract
The widely used Poisson count process in insurance claims modeling is no longer valid if the claims occurrences exhibit dispersion. In this paper, we consider the aggregate discounted claims of an insurance risk portfolio under Weibull counting process to allow for dispersed datasets. A copula is used to define the dependence structure between the interwaiting time and its subsequent claims amount. We use a Monte Carlo simulation to compute the higher-order moments of the risk portfolio, the premiums and the value-at-risk based on the New Zealand catastrophe historical data. The simulation outcomes under the negative dependence parameter θ, shows the highest value of moments when claims experience exhibit overdispersion. Conversely, the underdispersed scenario yields the highest value of moments when θ is positive. These results lead to higher premiums being charged and more capital requirements to be set aside to cope with unfavorable events borne by the insurers.
Highlights
The widely used Poisson count process in insurance claims modeling is no longer valid if the claims occurrences exhibit dispersion
The primary objective of an insurance company is to ensure that it can pay its promised obligations and remain solvent in the business. This can be achieved by managing surplus processes effectively and charging the appropriate premium amount, which will guarantee an adequate reserve and capital requirement to cope with any unfavorable events
We organize the remainder of this article as follows: In Section 2, we introduce the aggregate discounted claims model under Weibull counting process together with copulae to represent the dependency between the interwaiting time (IWT) and the subsequent claim sizes
Summary
The widely used Poisson count process in insurance claims modeling is no longer valid if the claims occurrences exhibit dispersion. The underdispersed scenario yields the highest value of moments when θ is positive These results lead to higher premiums being charged and more capital requirements to be set aside to cope with unfavorable events borne by the insurers. The primary objective of an insurance company is to ensure that it can pay its promised obligations and remain solvent in the business This can be achieved by managing surplus processes effectively and charging the appropriate premium amount, which will guarantee an adequate reserve and capital requirement to cope with any unfavorable events. Past studies related to the first two moments of the aggregate discounted claims were seen in Léveillé and Garrido (2001a) using renewal theory argument while, per Jang (2004), obtaining the Laplace transformation of the distribution using a different martingale approach. Past literature has relaxed the independence assumption used in the classical risk theory to include dependency elements between
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