Venter

Question 1

Correlations T-Test

Correlation T-Test

All Steps, Formulas, What is it?

Answer 1

Assumption #2: Losses in 1 AY are independent of losses in another AY

Evaluate whether age to age factors are independent (H0)
1. Calculate INCREMENTAL LDFs for 2 columns
2. Calculate correlation coefficient (r) using correl()
3. T = r * sqrt[ (n-2) / (1-r^2) ] with n = # of LDFs in a column
4. Look up t-statistic with dof = n-2
5. if T > t-stat, reject H0 –> LDFs for ___ and ___ are NOT independant

Question 2

Parameterized BF Method

Starting f(d) - seed

2 ways/formulas

Answer 2

If not given in the problem:
* = incremental LDF / CDF
* Incremental % Reported (first get % reported = 1/CDF)

Question 3

Parameterized BF Method

h(w) / f(w)

What is it? + both formula

Variance is assumed to be constant

Answer 3

h(w) ~ kind of like ultimate loss, but ONLY to be used with f(d) to get expected reserves
f(d) ~ incremental % reported

If variance assumed to be constant:
* h(w) = sumprod[ f(d), incremental loss ROWS] / sumSQ[ f(d) ]
* f(d) = sumprod[ h(w), incremental loss COLUMNS] / sumSQ[ h(w) ]

w for the years, d for development period

Question 4

Parameterized BF Method

h(w) / f(w)

What is it? + both formula

Variance is proportional to losses

Answer 4

h(w) ~ kind of like ultimate loss, but ONLY to be used with f(d) to get expected reserves
f(d) ~ incremental % reported

If variance assumed to be constant:
* h(w)^2 = sum[ incr loss^2 ROWS/ f(d) ] / sum[ f(d) ]
* f(d)^2 = sum[ incr loss^2 COLUMNS/ h(w) ] / sum[ h(w) ]
* Make incr loss^2 / f(d) and incr loss ^2 / h(w) triangles
* remember to take square root

w for the years, d for development period

Question 5

Superiority Test

Adjusted SSE

All formulas, which method is superior?

Answer 5

• Adj SSE = SSE / (n-p)^2
• SSE = sum(SSE Triangle) where each triangle entry is (Actual - Expected)^2 for incremental losses
• Model with lower adjusted SSE is superior

Question 6

Superiority Test

AIC / BIC

All formulas, which method is superior?

Answer 6

• AIC = SSE * exp(2p/n)
• BIC = SSE n^(p/n)
• SSE = sum(SSE Triangle) where each triangle entry is (Actual - Expected)^2 for incremental losses
• Model with lower AIC or BIC is superior

Question 7

SSE and Adjusted SSE

Answer 7

SSE Triangle = (Actual - Expected)^2
SSE = sum(SSE Triangle EXCLUDING 1ST COLUMN)
Adjusted SSE = SSE / (n-p)^2
where n = # of values in triangle excluding the first column
p = number of parameters

C-L and CC: p = d - 1
BF: p = 2d - 2
where d = # of development periods