Actuary Certification Credibility Theory 3

Question 1

The full credibility standard for pure premiums requires more expected claims than for claim frequency alone because:

Accepted Answer

Pure premiums depend on both frequency and severity, adding severity variance to total variance

Answer

Pure premiums are always larger numbers than raw frequencies

Answer

Insurance regulators impose stricter actuarial standards for premium filings

Answer

The normal approximation is less accurate for pure premiums than for counts

Question 2

If claim severity follows an exponential distribution (CV_S = 1.0), the full credibility standard for pure premiums at 90% confidence with ±5% accuracy requires approximately:

Accepted Answer

2,164 expected claims

Answer

1,082 expected claims

Answer

3,246 expected claims

Answer

4,328 expected claims

Question 3

Within a given risk (conditional on its parameter Θ), successive annual observations X₁, X₂, ..., Xₙ in the Bühlmann model are:

Accepted Answer

Conditionally independent and identically distributed given Θ

Answer

Positively correlated because later years depend on earlier claims

Answer

Negatively correlated through regression to the mean

Answer

Independent but NOT identically distributed given Θ

Question 4

The exact Bayesian credibility estimate equals the Bühlmann linear credibility estimate when:

Accepted Answer

The likelihood is from the exponential family with a conjugate prior (e.g., Poisson/Gamma, Normal/Normal)

Answer

The prior distribution is always uniform (flat)

Answer

The number of observations n is sufficiently large

Answer

The risk parameter Θ is observable

Question 5

A credibility premium is computed as P = Z × 250 + (1−Z) × 200 = 230. What is the credibility factor Z?

Accepted Answer

0.60

Answer

0.40

Answer

0.50

Answer

0.75

Question 6

For a portfolio of risks, estimated EVPV = 400 and estimated VHM = 500. What is Bühlmann's k?

Accepted Answer

0.80

Answer

1.25

Answer

0.45

Answer

1.60

Question 7

Using k = 0.80 from the portfolio above, a risk with n = 4 years of data has X̄ = 140 and the portfolio mean μ = 110. What is the Bühlmann credibility premium?

Accepted Answer

135.0

Answer

110.0

Answer

125.0

Answer

140.0