Sahasrabuddhe

Question 1

Model assumptions along with complexity (5)

Sahasrabuddhe

Answer 1

requires:

1. selection of a basic limit
2. use of a claim size model
3. claims data is adjusted to basic limit and common cost level
4. claim size models at maturities prior to ultimate (generally not available)
5. triangle of trend indices

1-3 - simple, 4-5 complex

Question 2

Convert losses in a triangle to a Base Layer B

Answer 2

C’_ij = C^L_ij x LEV(B;phi_n,j) / LEV(L;phi_ij)

n vs i means trended to year n

Question 3

Limited Expected Loss for an exponential distribution with limit L

Answer 3

LEV(L; theta) = theta * [1 - exp(-L/theta)]

Question 4

Development factor for any layer and any exposure period under simplified assumptions (layer lower bound <> 0)

Answer 4

= age-to-ultimate for common limit * ( 1 - U ) / ( 1 - R )

where U = LEV (X) / LEV (Y) at (i,n)
and R = LEV (X) / LEV (Y) at (i,j)

Question 5

Decay model for R

Answer 5

Rj (X,Y) = U + ( 1 - U ) * decay factor

decay factor = 0 at ultimate

Question 6

Name the 3 pieces of information we use to estimate
Rj(X, B)

Answer 6

• Ratio of actual losses in layer X to layer B on the
  diagonal
• Ratio of Limited Means at Ultimate (requires a
  distribution at Ultimate for each AY)
• Curve is near 1.000 at young ages

Question 7

What problem does using Rj(X, B), allow us to avoid

Answer 7

The full formula to convert LDF’s requires a
distribution of cumulative losses at each age.
By using Rj(X, B), we only need a distribution at
Ultimate.

Question 8

Steps to Calculate Base Layer LDFs

Answer 8

1. calculate trend factor in each cell of actual triangle (CY and AY trend)
2. determine unlimited paid to date mean in each cell (start with bottom row and trend up the column)
3. calculate limited mean in each cell
4. use limited means to convert actual triangle to Base Triangle, then calculate LDFs

Question 9

Convert Base Layer LDF to LDF at layer X

Answer 9

F^X_ij =
F^B_nj x [LEV(X; phi_i) / LEV(B; phi_n)] / [LEV(X; phi_ij) / LEV(B; phi_nj)]

phi_i is row i at ultimate
LEV ratios substitute for (b/d)/(a/c) = (b/a)/(d/c)
b and d will be right most column
c and d will be bottom most row

Question 10

What is U_i

Answer 10

Severity Relativity at Ultimate for AY i

LEV(X; phi_i)/LEV(B; phi_i)