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