Actuarial Notes

CAS Exam MAS-II Spring 2019, Question 8

Study guide: Exam MAS-II

You are using the Bühlmann-Straub approach to determine the credibility of the historical observations in order to estimate the number of claims in Year 3.

You are given:

  • The following table of insureds and claim counts per year:
Year Number of Insureds Number of Claims
1 P_1 N_1
2 P_2 N_2
  • The number of claims incurred per year for each insured is distributed as a Poisson random variable with mean \lambda.
  • \lambda follows a gamma distribution with shape parameter \alpha and rate parameter \theta.
  • The following three statements:

I. The credibility factor, Z, of the historical observations will change if \alpha changes and all other values remain constant. II. The credibility factor, Z, of the historical observations will change if \theta changes and all other values remain constant. III. The credibility factor, Z, of the historical observations will change if N_1 changes and all other values remain constant.

Determine which of the preceding statements are true.

  • A) I only
  • B) II only
  • C) III only
  • D) I, II and III
  • E) The answer is not given by (A), (B), (C), or (D)

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