SOA Exam FAM Sample Question 12
Study guide: Exam FAM
You are given the following information about a general liability book of business comprised of 2500 insureds:
(i) X_i = \sum_{j=1}^{N_i} Y_{ij} is a random variable representing the annual loss of the ith insured.
(ii) N_1, N_2, \ldots, N_{2500} are independent and identically distributed random variables following a negative binomial distribution with parameters r = 2 and \beta = 0.2.
(iii) Y_{i1}, Y_{i2}, \ldots, Y_{iN_i} are independent and identically distributed random variables following a Pareto distribution with \alpha = 3 and \theta = 1000.
(iv) The full credibility standard is to be within 5% of the expected aggregate losses 90% of the time.
Calculate the partial credibility of the annual loss experience for this book of business using limited fluctuation credibility theory.
- A) 0.34
- B) 0.42
- C) 0.47
- D) 0.50
- E) 0.53
Answer this question and see the worked solution
Concepts tested
- Partial Credibility
- Limited Fluctuation Credibility
- Full Credibility Standard
- Aggregate Loss Model
- Credibility