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Intensive Actuarial Training for Bulgaria January 2007. Lecture 6 – General Insurance Pricing and Reserving By Michael Sze, PhD, FSA, CFA. Overall Average Rate Changes. Loss Cost Method New Average Claim Cost = E[$L]/# exposure, where E[$L] is the Expected Claim Amount
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Intensive Actuarial Training for Bulgaria January 2007 Lecture 6 – General Insurance Pricing and Reserving By Michael Sze, PhD, FSA, CFA
Overall Average Rate Changes • Loss Cost Method • New Average Claim Cost = E[$L]/# exposure, where E[$L] is the Expected Claim Amount • New Average Gross Rate = New Average Claim Cost / PLR • Loss Ratio Method • Indicated Rate Change = E[LR]/PLR – 1, where • E[LR] = E[$L]/Current Rate x # exposure
Production of Manual Rates • Use the largest cell to be base cell • Its claim rate is the Base Rate (BR) • Claim rate of each other cell i is compared to BR, the ratio is called the differential di • Cells in each different risk class produces a vector of differentials
Changing Manual Rate Differentials di • Loss Ratio (LR) Method • Indicated di = Existing di x LRi / LRBase • If LRi = LRBase , existing di need not change • Loss Cost (LC) Method • Indicated di = LCi/LCBase • Note that LR not equal to LC
Balancing Back When Base Rate changes BRnew=BRold(1+) • New Ratei = Brnew x new di • However, this combination may be off-balance • because New Average d may not be equal to Old Average d • Balance back factor = Old Average d/New Average d
P&C Loss Reserving • Gross IBNR reserves is total of • Future development on known claims • Files closed but may be reopened • Pure IBNR • Claims reported, but not recorded
Paid and Incurred Loss Development • Paid-loss development factor (L.D.F.) = Cumulative paid @ durationj / Cumulative paid @ durationi – 1 • Incurred-loss development: • Same concept • Applied to incurred data (= paid-to-date + estimated reserve for outstanding claims)
Loss Reserving Methods • Case Reserve Estimates Plus • For each case, add Gross IBNR = pure IBNR + RBNR • Very subjective • Expected Loss Ratio (E[LR]) Method • Estimate ultimate E[LR] • E[$L] = E[LR] x earned premium • E[Loss Reserve] = E[$l] – [$L, paid-to-date]
Loss-Development Triangle Method • Historical data triangle of paid claims • Create a cumulative paid triangle • Calculate loss development factors LDF • Seek pattern to complete missing triangle • Reserve = E[ultimate paid] – [paid-to-date] • Same process can be done for incurred
Bornhuetter-Ferguson Method • A combination of E[LR] and LDF methods • For each accrual year, estimate E[LR] • E[$L,ultimate] = E[LR] x earned premium • E[Loss Reserve] = E[$L,ultimate](1-1/fult) • Where fult = fi
