A4

Question 1

Identify five advantages of a high deductible program.

Answer 1

Siewert 1. Achieves price flexibility while passing additional risk to larger insureds 2. Reduces residual market charges and premium taxes 3. Gives cash flow advantages to insureds 4. Provides incentive for insureds to control losses while protecting them from large losses 5. Allows self Insurance without subjecting insureds to demanding state requirements

Question 2

Briefly explain why we need to index limits for inflation when calculating development factors for various deductibles. Provide two methods for indexing the limits.

Answer 2

Siewert It keeps the proportion of deductible/excess losses constant about the limit from year to year. 1. Fit a line to average severity over a long term history 2. Use an index that reflects the movement in annual severity changes

Question 3

One option for estimating reserved for an excess layer is to use a distributional model. Briefly explain how a distributional model works.

Answer 3

Siewert It models the development process by determining distribution parameters that vary over time. Once the parameters are chosen we can calculate severity relativity s. Comparing these relativities over time results in development factors.

Question 4

One option for estimating reserved for an excess layer is to use a distributional model. Identify three methods for estimating the parameters of a distributional model.

Answer 4

Siewert 1. Method of moments 2. Maximum likelihood estimation 3. Siewert’s approach - minimize the chi-square between the actual and expected severity relativities around a particular deductible size.

Question 5

One option for estimating reserved for an excess layer is to use a distributional model. Provide two advantages of a distributional model.

Answer 5

Siewert 1. Provides consistent loss development factors 2. allows for interpolation among limits and years

Question 6

Explain why development for losses excess of aggregate limits decrease more rapidly over time with smaller deductibles then with larger ones

Answer 6

Siewert Aggregate limits only cover losses under the deductible. Since most of the later development occurs in the layers of loss above the deductible, excess of aggregate losses reach their ultimate value sooner for smaller deductibles

Question 7

Describe two ways to handle ALAE under a high deductible program

Answer 7

Siewert Approach 1: account manages expense itself (ie. ALAE not covered) - development patterns reflect losses only Approach 2: ALAE is treated as loss and subjected to applicable limits - development patterns reflect a combination of losses and expenses.

Question 8

Provide two advantages and one disadvantage of the implied development method

Answer 8

Siewert Advantages: 1. provides an estimate of excess losses at early maturities even when excess losses have not emerged. 2. Development factors for limited losses are more stable than those determined for excess losses. Disadvantage: does not explicitly recognize excess loss development

Question 9

Provide one advantage and two disadvantages of the direct development method

Answer 9

Siewert Advantage: explicitly recognizes excess loss development Disadvantages: 1. excess factors tend to be overly leveraged and extremely volatile. 2. if excess losses have not yet emerged, we can’t estimate IBNR.

Question 10

Provide two advantages and one disadvantage of the credibility-weighting method.

Answer 10

Siewert Advantages: 1. gives us the ability to tie into pricing estimates for recent years where excess losses have not emerged. 2. provides more stable estimates over time Disadvantage: ignores actual experience to the extent of the complement of credibility

Question 11

Provide two advantages and two disadvantages of the loss ratio method

Answer 11

Siewert Advantages: 1. can be used when no data is available or when data is immature. 2. Loss ration estimates can be consistently tied to pricing programs. Disadvantages: 1. ignores actual emerging experience. 2. may not properly reflect account characteristics since development may emerge differently due to the exposures written.

Question 12

Briefly describe three problems with the current application of trend rates

Answer 12

Sahasrabuddhe

1. Tend not to vary between accident periods
2. Trend that occurs in the development period or calendar period direction is often not considered
3. Tend not to vary by claims layer

Question 13

Identify two requirements of claim size models.

Answer 13

Sahasrabuddhe

1. Claim size model parameters can be adjusted for the impact of inflation
2. Limited expected values and unlimited means can be easily calculated

Question 14

In general, claims development patterns are estimated from unadjusted data and are applied to claims for all exposure periods. a) Briefly describe the assumptions underlying the statement above. b) Briefly describe any adjustments that must be made to the data when these assumptions are not met.

Answer 14

Sahasrabuddhe (removed from new questions)

Part a:

Assumes claims are provided on a ground-up unlimited basis and that only accident year trend exists

Part b:

Adjust the claims data for differences in cost level and limit using limited expected values

Question 15

State (in words) Sahasrabuddhe’s key finding.

Answer 15

Sahasrabuddhe Development factors at different cost levels and di↵erent layers are related to each other based on claim size models and trend

Question 16

Define R_j(X,B).

Answer 16

Sahasrabuddhe R_j(X,B) is the ratio between limited expected values for layer X and B at the end of development interval j

Question 17

Assuming that R_j (X, B) < 1, briefly describe three properties of R.

Answer 17

1) R_a >R_b, where a • There will be less development in the excess layer at early maturities

2 & 3) below

Question 18

Fully describe an alternative calculation of R.

Answer 18

An alternative calculation of R is R_j(X,B)=U+(1-U)·Decay Factor. The decay factors are determined using a decay model. The model ensures that R is “high” at early maturities (closer to 1) and “low” at later maturities (further from 1). At ultimate, the decay factor is 0 and R = U

Question 19

Discuss five assumptions that must be met in order to implement the reserving procedure (standard procedure, not the simplified version) described in the paper.

Answer 19

1. The procedure requires us to select a basic limit
   
   • When analyzing a loss triangle, actuaries make an implicit assumption that the limit associated with the triangle is credible. Thus, even if we select a basic limit, there is very little additional work involved
2. The procedure requires the use of a claim size model
   
   • Claim size models are typically available. In addition, since the primary goal of the claim size model is to obtain reasonable ratios of limited expected values to unlimited means, 100% accuracy is not required and a simple claim size model may be sufficient
3. The procedure requires that the data triangle be adjusted to a basic limit and common cost level
   
   • Given claim size and trend information, this is fairly simple to implement
4. The procedure requires claim size models at maturities prior to ultimate
   
   • Claim size models prior to ultimate are generally not available. However, since we only require the ratio of expected values to adjust development patterns from one layer to another, a robust claim size model is probably not required
5. The procedure requires a triangle of trend indices
   
   • Trend indices are dicult to calculate for cumulative claims because trend typically occurs on an incremental basis. In addition, trend indices are dicult to calculate for incurred claims (in particular, the timing of the e↵ect of trend on case reserves. We can avoid these issues if we assume no calendar year trend)