An Application Of Markov Chains And Mixed Poisson Distribution In Modelling No-Claim Discount Systems For Motor Insurance Data
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Date
2022-05
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University Of Ghana
Abstract
Most No-Claim Discount (NCD) systems are unfair to either one or both parties. Most systems are the simple random walk model, whereby in case of a claim, the policyholder moves down a discount level and vice versa. Modelling of data of claim amount is of paramount importance to manage risk reserve for payment of claims. Actuaries model uncertainty using probability distributions. The movements within the NCD systems are those of the in-between cases, and a fair NCD system, should take into consideration the frequency of claims and the non-homogeneity factor. In this study, the Markov chains have been employed to explain the movement between levels in the NCD system and mixed Poisson distribution to calculate the probabilities, with the mixing distributions been the exponential and the gamma, and Poisson models. The motor insurance claim data from Sweden was used in this study. The study found that the Geometric distribution model was better fitted to the observed claim frequencies in both the maximum likelihood estimation and method moments than the Poisson model. The results for the 3-Level NCD systems showed that the policyholders were rewarded with approximately 95% chances of moving to the next higher level towards attaining a no premium zone if a claim is not made in the cycle and were punished if a claim is made by dropping to the lower level with approximate probability of 0.048 and it was generally observed. The study found that due to the fairness of the system, policyholders who make claims are equally punished by dropping from their current level to the lower one or are made to stay in their current level in the next cycle. In conclusion, the multi-level NCD system was designed to reward policyholders who are extra vigilant on the road in terms of avoiding road accidents and penalized bad road users. The descriptive statistics of the claim frequency revealed that the number of claims by policyholders was right or positively skewed with a mean number of claims approximately zero (0.053).
Description
MPhil. Acturial Science
Keywords
Markov Chains, Mixed Poisson Distribution, Motor Insurance Data