Abstract
The aim of this study is to propose an estimation approach to non-life insurance claim counts related to the insurance claim counting process, including the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity and a beta-shaped intensity. The estimating function, such as the zero mean martingale (ZMM), is used as a procedure for parameter estimation of the insurance claim counting process, and the parameters of model claim intensity are estimated by the Bayesian method. Then,Λ(t), the compensator of N(t) is proposed for the number of claims in a time interval (0,t]. Given the process over the time interval (0,t]., the situations are presented through a simulation study and some examples of these situations are also depicted by a sample path relating N(t) to its compensatorΛ(t).
Highlights
In the field of non-life insurance, the modeling of claim counts is a very important component in a risk model with regard to loss reserving, pricing, underwriting, etc
The aim of this study is to propose an estimation approach to non-life insurance claim counts related to the insurance claim counting process, including the non-homogeneous Poisson process (NHPP) with a bell-shaped intensity and a beta-shaped intensity
We present an estimation approach to non-life insurance claim counts in the claim counting processes using an estimating function, the zero mean martingale (ZMM)
Summary
In the field of non-life insurance, the modeling of claim counts is a very important component in a risk model with regard to loss reserving, pricing, underwriting, etc. In 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). Studied the periodic risk model consisting of the claim counting process with a bell-shaped intensity function (called the Gaussian intensity) of the form. We present an estimation approach to non-life insurance claim counts in the claim counting processes using an estimating function, the zero mean martingale (ZMM). This approach provides a parameter estimator, ˆ t , of process, including the MLE for the parameter estimation of model claim intensity proposed by Jaroengeratikun et al [8]. The Bayesian analysis is used to estimate the parameters of model claim intensity
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