Quest for Optimal Bonus-Malus in Automobile Insurance in Developing Economies: An Actuarial Perspective

Abstract

This paper evaluates the bonus-malus system in practice in the Nigerian motor insurance industry. It would appear that the regulation is a bit fluid so that what actually looks like a bonus-malus system is more like a rule of thumb as operators do not honor the industry agreed tariff. This paper constructs an alternative bonus-malus scale that has reasonable penalties and that is yet commercially feasible. The model can easily be replicated for other developing economies.

An Alternative Pricing System through Bayesian Estimates and Method of Moments in a Bonus-Malus Framework for the Ghanaian Auto Insurance Market

“…Risk distributions and rating factors in insurance portfolios have hidden functions which vary with time and hence are understood to be well fitted by distributions such as the negative binomial, mixed Poisson, lognormal, etc. ; see Walhin and Paris (1997) and Ibiwoye et al (2011). As a result, policyholder's career, age, gender, marital status, the type and use of automobile, location of garage, and so on are always helpful in bringing the risk into homogeneous groups and rated a priori through generalized linear models (see Renshaw 1994;Pinquet 2000;Brouhns et al 2003;Kafkova and Krivankova 2014).…”

The Over-Searching Accidents Causative Factors in Ghana: The Role of Policyholders Education Levels

“…Despite these homogenous groupings, swiftness of reflexes, aggressiveness at the back of the wheel, or information on road safety regulations which have impact on frequency and severity of claims are always difficult to deal with by risk forecasters because of their heterogeneous nature (Brouhns et al, 2003;Ibiwoye et al, 2011;Kafkova & Krivankova, 2014;Kafková , 2015;Pinquet, 2000;Renshaw, 1994;Walhin & Paris, 1997). Policyholders or drivers also contributions to minimizing these risks are also in doubt since their level of understanding for instance road safety regulations, may highly depend on their level of education (Adedeji et al, 2016;Ibiwoye et al, 2011;Mock et al, 1999;Smart & Mann, 2002). To this effect, recent extensive study conducted by Al-Reesi et al (2013) essentially confirmed that risky driving and aggressively violation of road traffic laws in particular are the main risk factors for claims occurrences.…”

“…Therein, we draw upon the findings from Adedeji et al (2016), Al-Reesi et al (2013), Ibiwoye et al (2011), Mends-Brew et al (2019, Mock et al (1999), Plankermann (2013), Smart and Mann (2002), Smith (2005) and consider education, education levels as an independent and very uncommon variables for premium rating with the reason that Ghana have majority of road users with different levels of education. Education is the process of facilitating learning, or acquisition of knowledge, skills, values and habits or simply put is the process of helping someone to do things.…”

Bayesian Bonus-Malus Premium with Poisson-Lindley Distributed Claim Frequency and Lognormal-Gamma DistributedClaim Severity in Automobile Insurance

“…The exact loss occurring from each claim results in different premiums for policyholders with the same number of claims. The Bayesian bonus-malus premium that must be paid fairly for all policyholders in the portfolio is equal to the product of the Bayesian premium based both on the frequency component in (5) and the severity component in (11) and can be expressed by…”

“…Reference [10] considered both frequency and severity components in the design of an optimal BMS by assuming that claim frequency had a Geometric distribution (mixed Poison with Exponential distribution), and claim severity was Pareto distributed. Reference [11] considered the design of optimal BMS based on both frequency and severity components using mixed Poisson with Exponential distribution and mixed Poisson with Gamma for the frequency component. The number of claims was assumed to be Poisson distributed, while the underlying risk of each policyholder was taken to be Exponential and Gamma distributed called the prior distribution.…”