1. Intensive Actuarial Training for Bulgaria January 2007
Lecture 6 – General Insurance Pricing and Reserving
By Michael Sze, PhD, FSA, CFA

2. 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

3. 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

4. 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

5. 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

6. 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

7. Paid and Incurred Loss Development
Paid-loss development factor (L.D.F.) =
Cumulative durationj /
Cumulative durationi – 1
Incurred-loss development:
Same concept
Applied to incurred data (= paid-to-date + estimated reserve for outstanding claims)

8. 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]

9. 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

10. 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