CAS CAS Actuarial Modeling and Pricing Techniques 1 — Questions and Answers
Question 1: What is the 'pure premium' method for calculating insurance rates?
- Dividing projected ultimate losses by the number of exposures to derive the average loss cost per exposure unit (Correct answer)
- Dividing total premium by the number of policies in force
- Multiplying the loss ratio by the current average premium
- Calculating the ratio of incurred losses to earned premium
Correct answer: Dividing projected ultimate losses by the number of exposures to derive the average loss cost per exposure unit
The pure premium method directly derives a loss cost per exposure unit, which is then loaded for expenses and profit to produce the final rate.
Question 2: In actuarial ratemaking, what does 'on-leveling' premium data accomplish?
- Adjusting historical premium to reflect what it would have been at current rate levels (Correct answer)
- Removing the effect of inflation from historical loss data
- Credibility-weighting the insurer's own experience against industry data
- Projecting future premium volume based on historical growth trends
Correct answer: Adjusting historical premium to reflect what it would have been at current rate levels
On-leveling (or bringing premiums to current level) ensures historical premiums are comparable to current rates before computing historical loss ratios.
Question 3: What is the 'loss development factor' (LDF) used for in casualty actuarial work?
- To project reported or paid losses at an interim age to their ultimate settled value (Correct answer)
- To adjust losses for inflation between accident years
- To convert incurred losses to paid losses for cash flow projections
- To measure the ratio of large losses to total losses in a portfolio
Correct answer: To project reported or paid losses at an interim age to their ultimate settled value
Loss development factors (also called age-to-age factors) are derived from historical loss triangles and applied to immature losses to estimate ultimate claim costs.
Question 4: Which of the following best describes the Bornhuetter-Ferguson (BF) reserve method?
- A weighted blend of the development method and the expected loss method, giving credibility to both reported losses and an a priori expected loss estimate (Correct answer)
- A purely extrapolative method that relies solely on historical loss development patterns
- A frequency-severity method that multiplies claim counts by average severity
- A regression-based method using economic variables to predict ultimate losses
Correct answer: A weighted blend of the development method and the expected loss method, giving credibility to both reported losses and an a priori expected loss estimate
The BF method is valuable for immature accident years where little data exists, balancing observed development patterns with an independent a priori loss estimate.
Question 5: In GLM (Generalized Linear Model) ratemaking, what is the typical link function used for multiplicative rating plans?
- Log link function (Correct answer)
- Identity link function
- Logit link function
- Probit link function
Correct answer: Log link function
The log link function produces a multiplicative rating structure where rating factors for different variables multiply together, which is standard in P&C insurance pricing.
Question 6: What is 'credibility theory' used for in casualty actuarial pricing?
- To blend an insured's own experience with external data in proportion to the statistical reliability of the insured's data (Correct answer)
- To assess whether an actuary's reserve opinion is reliable enough to publish
- To measure how accurately a rating plan predicts future losses
- To determine whether an insurer's surplus is adequate to write new business
Correct answer: To blend an insured's own experience with external data in proportion to the statistical reliability of the insured's data
Credibility theory assigns a weight Z to an insured's own data (0 ≤ Z ≤ 1) based on its volume and homogeneity, blending it with broader complement-of-credibility data.
CAS CAS Actuarial Modeling and Pricing Techniques 1
What is the 'pure premium' method for calculating insurance rates?