Abstract
This study presents an estimation approach to non-life insurance claim counts relating to a specified time. The objective of this study is to estimate the parameters in non-life insurance claim counting process, including the homogeneous Poisson process (HPP) and the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity. We use the estimating function, the zero mean martingale (ZMM) as a procedure of parameter estimation in the insurance claim counting process. Then, Λ (t), the compensator of N (t) is proposed for the number of claims in the time interval (0, t]. We present situations through a simulation study of both processes on the time interval (0, t]. Some examples of the situations in the simulation study are depicted by a sample path relating N (t) to its compensator Λ (t). In addition, an example of the claim counting process illustrates the result of the compensator estimate misspecification.
Highlights
Nowadays, insurance is a common way of managing risks and the insurance industry has grown rapidly over time
The objective of this study is to estimate the parameters in non-life insurance claim counting process, including the homogeneous Poisson process (HPP) and the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity
Some authors have found an alternative approach to claim counts relating to a specified time or their behavior over time, for example, Mikosch [5] viewed the claim counting process as a homogeneous Poisson process (HPP) in the Cramér-Lundberg model, one of the most popular and useful risk models in non-life insurance, and Matsui and Mikosch [6] considered a Poisson cluster model for the modeling of a total claims amount by a point of claim counts as an HPP with a constant rate of occurrence called the constant intensity
Summary
Insurance is a common way of managing risks and the insurance industry has grown rapidly over time. Bühlmann [3,4] presented the credibility approach in the form of a linear function to estimate and predict the expected claim counts in upcoming periods, using past experience of claims as a risk class or related risk classes. For some non-life insurance portfolios, the claim counts during a time period are caused by periodic phenomena or seasonality These claim counts are modeled in terms of a non-homogeneous Poisson process (NHPP) with a period time-dependent intensity rate. Morales [7] presented the periodic risk model consisting of the claim counting process with a bell-shaped intensity function (called the Gaussian intensity) of the form t. We will present an estimation approach to non-life insurance claim counts related to a specification of the two different claim counting processes, i.e., HPP, and NHPP with a bell-shaped intensity function, through a simulation study. An estimating function, such as the zero mean martingale (ZMM), is used here as a procedure of parameter estimation of an insurance claim counts model, and the parameters of model intensity are estimated by the MLE method
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