Clark

Question 1

Advantages/Disadvantages of Using Parameterized Curves

Answer 1

Advantages:
* Only need to estimate 2 parameters
* Allows use of data not strictly from a triangle with evenly spaced evaluation dates
* Final indicated pattern is a smooth curve

Disadvantages
* Will not work if there is expected negative development (ex. significant salvage recoveries)

Question 2

Assumptions of Clark Model

Answer 2

1. Incremental losses are independent and identically distributed (IID)
   One period does not affect surrounding periods (inflation, legal trends violate this) and emergence pattern same for all AYs
2. Variance / mean (σ^2) is fixed and known
3. Variance estimates are based on an appromixation to the Rao-Cramer lower bound

Question 3

Weibull / Loglogistic G(x)

What is G(x)

Answer 3

G(x) = % reported
Weibull G(x) = 1 - exp(-(x/θ)^ω)
Loglogistic G(x) = x^ω / (x^ω + θ^ω)

Question 4

Process Variance

What is it + formula

Answer 4

Variance due to random flucations caused by unpredictability of insurance

Process variance of reserves =σ^2 * sum of reserves
Process variance of prospective losses = σ^2 * expected loss

Question 5

Parameter Variance

What is it + formula

Answer 5

Variance due to uncertainty in our estimators

Parameter variance of reserves = calculated based on Rao-Cramer approx (usually given)

Parameter variance of prospective losses = Var(Prem * ELR) = EP^2 * Var(expected loss)

Question 6

Process Variance/Mean Ratio

σ^2 Formula

Answer 6

aka variance / mean
= sum(chi sq triangle) / (n-p)
n = # entries in triangle
p = # of AYs + 2 | 3 for Cape Cod (ELR, θ, ω)

Question 7

Standard Deviation / Coefficient of Variation (CV)

Formula

Answer 7

SD= sqrt(Process Variance + Parameter Variance)
=sqrt(process SD ^2 + parameter SD ^2)

CV of Reserves = SD / sum(reserves)
CV of Prospective Losses = SD / Expected Losses

Question 8

Normalized Residual / Chi Square

Formula

Answer 8

Normalized Residual = Actual - Expected / sqrt(σ^2 * Expected)
Chi Square = (Actual - Expected)^2 / Expected

Question 9

Loglikelihood / MLE Triangle

Answer 9

MLE Triangle = Actual * ln(Expected) - Expected
Loglikelihood = sum (MLE triangle)

Question 10

Expected Incremental Loss Triangle

Formula for LDF and Cape Cod method

Answer 10

LDF Method = Ult Loss * [G(x) - G(x-12)]
=Truncated Ult Loss * Truncated [G(x) - G(x-12)]

Cape Cod Method = ELR Ult * [G(x) - G(x-12)]