BAIC 6 - Advanced Ratemaking and Professionalism

Question 1

Probability Density Function (PDF)

Answer 1

Describes density of the outcome of a random variable X, theoretically equivalent of a histogram of empirical data
Ex: Loss severity distribution - skewed because large losses are fewer in number, but make up a significant amount of total dollars of loss

Question 2

Cumulative Distribution Function (CDF)

Answer 2

Describes the probability that a random variable X takes on values less than or equal to x

Question 3

The Lee Diagram

Answer 3

1. Switching the axes of the CDF to imagine the loss distribution
   S(x) or G(X) = 1-x
2. Has the same shape as a representative sample from the distribution, sorted by size and equally spaced

Question 4

Expected Value

Answer 4

Mean, mu, first raw moment; average value of a random variable = integral of S(x) where S(X) = 1- F(x)

Question 5

Basic Limits aggregation

Answer 5

1. Losses are restated as if all policies were purchased at the basic limit.
2. Basic limit is usually the financial responsibility limit or a commonly selected limit
3. ALAE is not capped

Question 6

Increased Limits data aggregation

Answer 6

1. Losses are limited to a higher limit

2. ALAE remains unlimited

Question 7

Limit Loss Cost Reviews and Pricing

Answer 7

Basic limit loss costs are reviewed and filed on a regular basis (perhaps annually)
1. A larger volume of losses capped at the basic limit can be used for a detailed experience analysis
2. Experience is more stable since large, volatile losses are capped and excluded from the analysis;
Higher limits are reviewed less frequently
1. Requires more data volume
2. Fewer policies are written at higher limits
3. Large losses are highly variable
*The two approaches are used together to price a book of business at various policy limits

Question 8

Increased limits ratemaking process

Answer 8

Developing charges for expected losses at higher limits of liability
Usually results in a multiplicative factor to be applied to basic limits loss cost, increased limit factor (ILF)

Question 9

Increased Limit Factor

Answer 9

ILF(k) = Expected Pure Premium at Policy limit k / Expected Pure Premium at Basic Policy Limit
or
E[X^k] / E[X^b]

Question 10

Assumptions to modify the ILFformul

Answer 10

Frequency is assumed to be independent of severity and policy limit

Question 11

Size of Loss Method

Answer 11

1. Individual losses are grouped by size into redetermined intervals
2. The aggregate loss within each interval is limited, if necessary, to the limit being reviewed
3. ALAE is added to the aggregate limit loss
   E[X^k] = (losses on claims up to k + k * number of claims above k + total ALAE) / total number of claims

Question 12

Layer Method

Answer 12

1. Individual losses are sliced into layers
2. Fro each loss, the amount of loss corresponding to each layer is added to the aggregate for that layer
3. The aggregate loss for each layer up to the limit is added together
4. ALAE is added to the aggregate limited loss
   E[X^k] = (sum of all losses in each layer up to k + ALAE) / total claims

Question 13

Size Method advantages and disadvantages

Answer 13

Advantages: 1) Conceptually Straightforward; 2) Data can be used in calculations immediately; 3) More complicated integral is actually generally easier to calculate
Disadvantages: 1) Computationally intensive for calculating sets of increased limits factors

Question 14

Layer Method advantages and disadvantages

Answer 14

Advantages: 1) Computationally simple for calculating sets of increased limits factors; 2) no integration disadvantage when data is given numerically (generally the case)
Disadvantages: 1) Unintuitive; 2) Data must be processed so that it can be used in calculation; 3) S(x) is generally a more difficult function to integrate

Question 15

The Consistency Rule

Answer 15

1. Each layer represents the additional marginal cost for higher limits and cannot be larger than any lower layers
2. Marginal premium per dollar of coverage should decrease as the limit of coverage increases
   - ILFs should increase at a decreasing rate
   - Expected costs per unit of coverage should not increase in successively higher layers
   - For example: change in ILF / change in Limit should decreases as limit grows

Question 16

Loss Elimination Ratio (LER)

Answer 16

1. Savings associated with use of deductible
2. Equal to proportion of ground up losses eliminated
   LER(j) = E[X^j] / E[X]
   E[X^j] = Expected losses below deductible j (limited expected losses)
   E[X] = Expected ground-up losses (full value property or total limits liability)

Question 17

Deductible Relativities

Answer 17

1. Deductible analogue of an increased limits factor
2. Factor applied to the base premium to reflect a deductible

DR(j) = (1 0 LER( j ) ) / ( 1 - LER(base) )

Question 18

Dependency factor for relativity

Answer 18

Depends on:

1. Loss elimination ratio of the base deductible
2. Loss elimination ratio of the desired deductible

Question 19

Problems with construction - censorship and truncation

Answer 19

Censorship - amounts are known to equal or exceed the policy limit, but their values are capped at the policy limit; Right censorship (from above) occurs when a loss exceeds the policy limit; the loss is known, but its value is recorded as the policy limit amount
Truncation - events are undetected and their values are completely unknown; Left truncation (from below) occurs when a loss below the deductible is not reported
**Data is sparse at higher limits

Question 20

Fitted distribution to severity function

Answer 20

Data can be used to fit the severity function to a probability distribution

Question 21

Fitted distributions - addresses concerns

Answer 21

1. ILFs can be calculated for all policy limits
2. Empirical data can be smoothed
3. Trend
4. Payment lag

Question 22

ISO uses these fitted distributions

Answer 22

Truncated Pareto

Mixed exponential

Question 23

Policy Rating Formula

Answer 23

LC = Terr.LC x ILF x (PCF + SCF) x discounts
LC = final loss cost
Terr.LC = territorial base loss cost
ILF = increased limits factor
PCF = primary class factor
SCF = secondary classs factor

Question 24

Basic Policy Rating vs Extension of Exposures

Answer 24

The policy rating procedure is used to determine the premium for individual exposures
The same procedure is used in the extension of exposures ratemaking methodology
-Exposure detail must be collected through statistical reporting
-The statistical records are used in conjunction with the current manual rates to determine the current premium for the exposures in the experience period
-In practice, some modifications may be made

Question 25

Modifications made between policy rating and extensions of exposures

Answer 25

1. For basic limit ratemaking, substitute the basic limit for the actual limit used on the policy
2. At ISO, we use the manual loss costs and factors instead of the rates and factors actually used by individual insurers
3. Many insurers deviate from ISO loss costs
4. The LCCL we use for ratemaking is not the reported premium