September 2012
Beginner to intermediate
536 pages
14h 40m
English
book
Loss Models: From Data to Decisions, 4th Edition
by Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot
Content preview from Loss Models: From Data to Decisions, 4th Edition
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19.5 Exercises
19.1 Past claims data on a portfolio of policyholders are given in Table 19.4. Estimate the Bühlmann credibility premium for each of the three policyholders for year 4.
Table 19.4 Data for Exercise 19.1.
19.2 Past data on a portfolio of group policyholders are given in Table 19.5. Estimate the Bühlmann–Straub credibility premiums to be charged to each group in year 4.
Table 19.5 Data for Exercise 19.2.
19.3 For the situation in Exercise 17.3, estimate the Bühlmann credibility premium for the next year for the policyholder.
19.4 Consider the Bühlmann model in Example 19.1.
(a) Prove that Var(Xij) = a + v.
(b) If {Xij : i = 1, …, r and j = 1, …, n} are unconditionally independent for all i and j, argue that an unbiased estimator of a + v is
(c) Prove the algebraic identity
(d) Show that, conditionally,
(e) Comment on the implications of (b) and (d).
19.5 Suppose that the random variables Y1, …, Yn are independent with
Define b = b1 + b2 + ··· + bn and = ∑nj
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