Abstract
This paper examines the current No-Claim Discount (NCD) system used in Ghana’s auto insurance market as inefficient and outmoded and, therefore, proposes an alternative optimal Bonus-Malus System (BMS) intended to meet the present market conditions and demand. It appears that the existing BMS fails to acknowledge the frequency and severity of policyholders’ claims in its design. We minimized the auto insurance portfolios’ risk through Bayesian estimation and found that the risk is well fitted by gamma, with the claim distribution modeled by the negative binomial law with the expected number of claims (a priori) as 14%. The models presented in this paper recognize the longevity of accident-free driving and fully reward higher discounts to policyholders from the second year when the true characteristics of the hidden risks posed to the pool have been ascertained. The BMS finally constructed using the net premium principle is very optimal and has reasonable punishment and rewards for both good and bad drivers, which could also be useful in other developing economies.
Highlights
The role of the insurance market for economic growth and development can never be underestimated; see, for example, Stojakovicand Jeremic (2016)
Nii Anang Laryea (2016) found that unlike other countries where auto insurance business is well developed to the level that insurers use parameters such as the age of the auto and the claim history of the policyholder to predict risk, auto insurance premiums in Ghana use tariff guide from the National Insurance Commission (NIC)
The Bonus-Malus System (BMS) obtained using the models proposed in this work does modify the discounts made in the absence of claims
Summary
The role of the insurance market for economic growth and development can never be underestimated; see, for example, Stojakovicand Jeremic (2016). In this paper, following Denuit and Dhaene (2001), Bolancé et al (2007), Dorina et al (2007), and Ibiwoye et al (2011), we consider the negative binomial model, seen as a Poisson mixture distribution with gamma mixing, for claim count for auto insurance data in Ghana to obtain an optimal pricing system for the industry. With this probability law, it allows for serial dependence count of claims where gamma-distributed hidden individual non-homogenous variables are introduced.
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