Actuary Certification Actuary Certification Loss Models 2

Question 1

The Bühlmann credibility formula for the credibility estimate is:

Accepted Answer

Z · X̄ + (1−Z) · μ

Answer

The Bühlmann credibility estimate is Z·X̄ + (1−Z)·μ, a weighted blend of the observed mean X̄ and the prior mean μ, where Z = n/(n+k) is the credibility factor.

Question 2

In the Bühlmann credibility model, the credibility factor Z = n/(n+k) where k equals:

Accepted Answer

Expected process variance / variance of hypothetical means

Answer

k = v/a where v is the expected value of the process variance (EVPV) and a is the variance of the hypothetical means (VHM), so k = EVPV/VHM.

Question 3

Which reinsurance arrangement has the reinsurer paying losses above an attachment point up to a maximum layer?

Accepted Answer

Excess of loss (per-occurrence) reinsurance

Answer

Per-occurrence excess of loss reinsurance covers losses above the cedant's retention (attachment point) up to a specified maximum per single occurrence.

Question 4

The method of moments estimator equates sample moments to theoretical moments. For a one-parameter distribution, this means setting:

Accepted Answer

Sample mean = theoretical mean

Answer

With a single parameter, method of moments sets the sample mean equal to the theoretical mean E[X] and solves for the parameter.

Question 5

Which goodness-of-fit test statistic compares the squared differences between observed and expected frequencies divided by expected frequencies?

Accepted Answer

Chi-square statistic

Answer

The chi-square goodness-of-fit statistic is Σ(Oi − Ei)²/Ei, measuring the discrepancy between observed and expected cell frequencies.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Actuary Certification Loss Models 2