Reconciling two conflicting loss-cost reports
An insurer prepares a simplified loss-cost report for a clearly defined annual portfolio. The policy table contains one thousand earned policy-years. A claim table lists eighty included claims and two hundred forty thousand dollars of matching gross loss. A separate recovery table records forty thousand dollars, but the first analyst uses gross severity while the second silently subtracts recoveries. Their presentations use the same label, pure premium, even though the loss bases differ. A third report joins every payment transaction to a policy and sums exposure without checking whether policies repeat. The project sponsor wants a defensible baseline before a more complex predictive model is proposed. The analyst must identify which quantities are comparable and document how the reporting definition affects each result.
1. Calculate matching gross frequency, severity, and pure premium.
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Frequency is eighty divided by one thousand, or 0.08 claims per policy-year. Gross severity is 240,000 divided by eighty, or 3,000 dollars per claim. Their product gives gross pure premium 240 dollars per policy-year, matching gross loss divided by exposure.
2. How should net loss and join integrity be handled?
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If the stated recovery definition is appropriate, net total is 200,000 dollars and net loss per exposure is 200 dollars. Label that basis explicitly rather than mix it with gross severity. Reconcile row cardinality and policy-level exposure before aggregation so payment multiplicity does not duplicate exposure.