Sahasrabuddhe

Question 1

Briefly describe three problems with the current application of trend rates.

Answer 1

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

Question 2

Identify two requirements of claim size models.

Answer 2

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

Question 3

State (in words) Sahasrabuddhe’s key finding.

Answer 3

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

Question 4

Define Rj(X, Y ).

Answer 4

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

Question 5

Assuming that Rj(X, Y )

Answer 5

⇧ Ra > Rb, where a = U, where U = lim(a->infinity)Ra • U is simply Rj at ultimate. In this paper, we are not considering tail factors so U = Rn. Similar to the first property, Ra = U because there is more development associated with the denominator of R (claims in layer Y ) than the numerator of R (claims in layer X). ⇧ If Y = GUU AND if all development in the unlimited layer occurs above X, then the maximum value for R is calculated as U times the unlimited claims development factor.

Question 6

Fully describe an alternative calculation of R.

Answer 6

An alternative calculation of R is Rj(X, Y ) = 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 7

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 7

•The procedure requires us to select a basic limit •The procedure requires the use of a claim size model •The procedure requires that the data triangle be adjusted to a basic limit & common cost level •The procedure requires claim size models at maturities prior to ultimate •The procedure requires a triangle of trend indices

Question 8

Fully describe the steps underlying the reserving procedure (standard procedure, not the simplified version) described in the paper.

Answer 8

Question 9

Formula to convert losses in a triangle to a Base Layer
B

Answer 9

Question 10

Answer 10

Question 11

Steps to Calculate Base Layer LDFs

Answer 11

1. Calculate Trend Factor in each cell of Actual Triangle (CY and AY Trend)
2. Determine Unlimited Paid-to-Date Mean in each cell (Do this by using mean from last row, and trending up the column)
3. Calculate the Limited Mean in each cell 4. Use the Limited Means to convert Actual Triangle to Base Triangle, and calculate LDFs

Question 12

Convert Base Layer LDF to LDF at layer X

Answer 12

Question 13

Shortcut formula to convert Base Layer LDF to LDF at
layer X

Answer 13

Question 14

Answer 14

• 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 15

What does this term Rj(X, B) represent?

Answer 15

Question 16

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

Answer 16

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.