In this paper, a formula for calculating a premium for reinsurance is presented. This formula was determined by incorporating a lognormal-burr probability distribution model into the PH-transform principle which is one of the risk-adjusted premium calculating principles. The lognormal-burr probability distribution model was selected, modelled, classified and validated as the best fitting model to 2016 GAM’s automobile insurance claims data among the eight candidates of composite lognormal probability distribution models. Then, the formula was applied in calculating reinsurance premiums for an automobile insurance branch under an excess of loss non-proportional reinsurance treaty.
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