Application of Bühlmanns-Straub Credibility Theory in Determining the Effect of Frequency-Severity on Credibility Premium Estimation
The study sought to demonstrate how credibility claim costs without the consideration of claim frequency and claim severities underlined by different risk profiles underestimate claim costs or premiums charged policyholders by non-life insurance companies. We used secondary data of non-life marine insurers in Ghana, claim histories that range from the period of 2013 to 2018. The claim histories included claim sizes, claim counts and policy counts. Bühlmans-Straub Credibility theory model was used in estimating credibility weights, credibility claim costs, credibility claim frequencies and credibility claim severities and subsequently find the credibility frequency-severity claim cost as the product of credibility claim frequency and severity for the individual and respective risk classes. We compared the estimates of the claim costs or premiums and have observed that the credibility claim costs underestimates claim costs or the average claim costs compared to the credibility frequency-severity claim costs for most of the risk classes. This is an indication of how a lack of consideration for variability or unstableness of claim frequencies and severities with different risk profiles undermine claim costs estimated through credibility rate makings in insurance. The study recommends that credibility ratemaking by insurance companies based on inadequate claim history and or with enough class risk variation should include credibility risk frequency and severity for the determination of credibility risk premiums.