Sahasrabuddhe

Question 1

what is the purpose of the Sahasrabuddhe paper?

Sahasradbuddhe

Answer 1

to demonstrate the relationship between claims development, trend, and claim size factors

Question 2

what does Pinto/Gogol’s paper focus on when estimating XS layer dev.?

(Sahasradbuddhe)

Answer 2

fitting observed dev. factors based on a large industry database

Question 3

what are difficulties with Pinot/Gogol’s method to estimate excess layer development?

(Sahasradbuddhe)

Answer 3

• access to industry data may be difficult

- methodology doesn’t use inherent relationship between claims size models, trend and claims development patterns

Question 4

what are characteristics of trend rates in practice today?

Sahasradbuddhe

Answer 4

• refer to annual change in cost level for a claims layer
• tend not to vary between accident periods or claims layer
• trend in dev. or calendar period direction often not considered

Question 5

how does the author apply cost level indices?

Sahasradbuddhe

Answer 5

apply to cumulative ground-up unlimited claims

Question 6

what distribution is used to describe claim sizes?

Sahasradbuddhe

Answer 6

exponential

Question 7

what are two requirements of the claim size model?

Sahasradbuddhe

Answer 7

• params can be adjusted for inflation

- limited expected values and unlimited means can be easily calculated

Question 8

what must we do before determining development patterns for various layers and exposure periods?

(Sahasradbuddhe)

Answer 8

-adjust raw data to a basic limit at the latest exposure period

Question 9

what does the basic limit represent?

Sahasradbuddhe

Answer 9

the limit in which we have sufficient credibility to determine stable/accurate development patterns

Question 10

what is the difference between the standard CL factors and adjusted CL factors driven by?

(Sahasradbuddhe)

Answer 10

the size of the claim size parameters

Question 11

what happens when claim size parameters increase?

Sahasradbuddhe

Answer 11

-higher percentage of losses will be capped at the limit -> larger difference in limited expected values between the basic limit and limit of the data in the triangle

Question 12

what will cause the difference between the standard CL and adjusted factors to increase?

(Sahasradbuddhe)

Answer 12

• higher trend rates (highly negative OR positive)

- longer dev. patterns (i.e. long-tailed lines)

Question 13

why are Sahasrabuddhe’s adjusted development factors an improvement over the standard CL factors?

(Sahasradbuddhe)

Answer 13

demonstrates that dev. factors at different cost levels and different layers are related to each other based on claim size models and trend

Question 14

how might we deal with missing cost levels?

Sahasradbuddhe

Answer 14

-assume cost is equal to that of the latest exposure period

Question 15

what is a simplifying assumption about claim size?

Sahasradbuddhe

Answer 15

claim size models are only available at ultimate

Question 16

when is the impact of trend immaterial?

Sahasradbuddhe

Answer 16

when calculating ratios of LEV

Question 17

what does assuming R_j(X,B) < 1 imply?
[where R_j(X,B) = LEV(X_i,j)/LEV(B_i,j)

(Sahasradbuddhe)

Answer 17

implies that X is smaller than the basic limit B

Question 18

what three properties do we obtain by assuming R_j(X,B) < 1?
[where R_j(X,B) = LEV(X_i,j)/LEV(B_i,j)

(Sahasradbuddhe)

Answer 18

• R_a > R_b, where a < b (dev periods)
• R_a >= U, where U = lim(R_a) as a -> infinity
• If B = GUU AND all dev. in unlimited layer occurs above X, then the maximum value for R is calculated as U * unlimited claims dev. factor

Question 19

what can we expect for R_j at early maturities?

Sahasradbuddhe

Answer 19

there will be less development in the excess layer, resulting in an R ratio close to 1

Question 20

why does assuming R_j(X,B) < 1 imply that R_a >= U?
(where U = lim(R_a) as a -> inf

(Sahasradbuddhe)

Answer 20

there is more development associated with the denominator of R (claims in layer B) than the numerator of R (claims in layer X)

Question 21

when will the three conditions resulting from assuming R_j(X,B) < 1 be violated?

(Sahasradbuddhe)

Answer 21

• if there is negative dev.

- if we assume an excess layer may develop more quickly than a working layer

Question 22

how would decay factors be determined/calibrated?

Sahasradbuddhe

Answer 22

using observed ratios at each development period

Question 23

what are three assumptions of Sahasrabuddhe’s model that are easy to implement?

(Sahasradbuddhe)

Answer 23

1-requires us to select a basic limit
2-requires the use of a claim size model
3-data triangle must be adjusted to a basic limit and common cost level

Question 24

why doesn’t the claim size model need to be 100% accurate?

Sahasradbuddhe

Answer 24

-primary goal is to obtain reasonable ratios of limited expectations to unlimited means at higher values -> less important that the absolute LEVs be completely accurate

Question 25

what are two assumptions of Sahasrabuddhe’s model that are difficult to implement?

(Sahasradbuddhe)

Answer 25

1-requires claim size models at maturities prior to ultimate

2-requires a triangle of trend indices

Question 26

what is a benefit of creating claim size models over time?

Sahasradbuddhe

Answer 26

-provide an increased understanding of excess layer development

Question 27

why is it difficult to develop a triangle of trend indices?

Sahasradbuddhe

Answer 27

• trend indices specify cost level associated with cumulative claims, but trend typically occurs on an incremental basis
• impact of trend on reported incurred claims is difficult to quantify (particularly the timing of the effect of trend on case reserves)

Question 28

how can we avoid issues with developing a triangle of trend indices?

(Sahasradbuddhe)

Answer 28

-assume development only occurs in the exposure period direction (i.e. no CY trend)

Question 29

what is a benefit of directly confronting and documenting trend assumptions?

(Sahasradbuddhe)

Answer 29

-produces greater transparency and better informs the consumer of actuarial information