Sahasrabuddhe Flashcards
what is the purpose of the Sahasrabuddhe paper?
Sahasradbuddhe
to demonstrate the relationship between claims development, trend, and claim size factors
what does Pinto/Gogol’s paper focus on when estimating XS layer dev.?
(Sahasradbuddhe)
fitting observed dev. factors based on a large industry database
what are difficulties with Pinot/Gogol’s method to estimate excess layer development?
(Sahasradbuddhe)
- access to industry data may be difficult
- methodology doesn’t use inherent relationship between claims size models, trend and claims development patterns
what are characteristics of trend rates in practice today?
Sahasradbuddhe
- 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
how does the author apply cost level indices?
Sahasradbuddhe
apply to cumulative ground-up unlimited claims
what distribution is used to describe claim sizes?
Sahasradbuddhe
exponential
what are two requirements of the claim size model?
Sahasradbuddhe
- params can be adjusted for inflation
- limited expected values and unlimited means can be easily calculated
what must we do before determining development patterns for various layers and exposure periods?
(Sahasradbuddhe)
-adjust raw data to a basic limit at the latest exposure period
what does the basic limit represent?
Sahasradbuddhe
the limit in which we have sufficient credibility to determine stable/accurate development patterns
what is the difference between the standard CL factors and adjusted CL factors driven by?
(Sahasradbuddhe)
the size of the claim size parameters
what happens when claim size parameters increase?
Sahasradbuddhe
-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
what will cause the difference between the standard CL and adjusted factors to increase?
(Sahasradbuddhe)
- higher trend rates (highly negative OR positive)
- longer dev. patterns (i.e. long-tailed lines)
why are Sahasrabuddhe’s adjusted development factors an improvement over the standard CL factors?
(Sahasradbuddhe)
demonstrates that dev. factors at different cost levels and different layers are related to each other based on claim size models and trend
how might we deal with missing cost levels?
Sahasradbuddhe
-assume cost is equal to that of the latest exposure period
what is a simplifying assumption about claim size?
Sahasradbuddhe
claim size models are only available at ultimate
when is the impact of trend immaterial?
Sahasradbuddhe
when calculating ratios of LEV
what does assuming R_j(X,B) < 1 imply?
[where R_j(X,B) = LEV(X_i,j)/LEV(B_i,j)
(Sahasradbuddhe)
implies that X is smaller than the basic limit B
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)
- 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
what can we expect for R_j at early maturities?
Sahasradbuddhe
there will be less development in the excess layer, resulting in an R ratio close to 1
why does assuming R_j(X,B) < 1 imply that R_a >= U?
(where U = lim(R_a) as a -> inf
(Sahasradbuddhe)
there is more development associated with the denominator of R (claims in layer B) than the numerator of R (claims in layer X)
when will the three conditions resulting from assuming R_j(X,B) < 1 be violated?
(Sahasradbuddhe)
- if there is negative dev.
- if we assume an excess layer may develop more quickly than a working layer
how would decay factors be determined/calibrated?
Sahasradbuddhe
using observed ratios at each development period
what are three assumptions of Sahasrabuddhe’s model that are easy to implement?
(Sahasradbuddhe)
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
why doesn’t the claim size model need to be 100% accurate?
Sahasradbuddhe
-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
