25. Data on annual aggregate claims ($000's) for each of three employer liability risks over five years is given in Table 5.13. Here Yij denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 4 5 Yi (Yij – Y;)² - 1 2 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 3 4,382 5,028 4,434 4,844 5,642 4,866 2,180,690 1,190,476 1,049,784 (a) Using Model 1 of empirical Bayes credibility, calculate the credi- bility factor and credibility premium for next year for each of the three risks. 190 NO CLAIM DISCOUNTING IN MOTOR INSURANCE (b) Suppose now that you also have a risk volume denoted Pij corre- sponding to each Yij above. Some summary statistics for the risk volumes are as follows: 5 Risk Pij 1 1 3,560 2 2,276 3 4,012 In using Model 2 for empirical Bayes credibility theory, the credi- bility premium per unit of risk volume for next year for risk 1 has been calculated to be 6.46. Calculate the credibility premium per unit of risk volume for next year for risks 2 and 3.
25. Data on annual aggregate claims ($000's) for each of three employer liability risks over five years is given in Table 5.13. Here Yij denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 4 5 Yi (Yij – Y;)² - 1 2 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 3 4,382 5,028 4,434 4,844 5,642 4,866 2,180,690 1,190,476 1,049,784 (a) Using Model 1 of empirical Bayes credibility, calculate the credi- bility factor and credibility premium for next year for each of the three risks. 190 NO CLAIM DISCOUNTING IN MOTOR INSURANCE (b) Suppose now that you also have a risk volume denoted Pij corre- sponding to each Yij above. Some summary statistics for the risk volumes are as follows: 5 Risk Pij 1 1 3,560 2 2,276 3 4,012 In using Model 2 for empirical Bayes credibility theory, the credi- bility premium per unit of risk volume for next year for risk 1 has been calculated to be 6.46. Calculate the credibility premium per unit of risk volume for next year for risks 2 and 3.
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.58TI: What is the total effect on the economy of a government tax rebate of $500 to each household in...
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Transcribed Image Text:25. Data on annual aggregate claims ($000's) for each of three employer
liability risks over five years is given in Table 5.13. Here Yij denotes
claims in year j for risk i.
TABLE 5.13
Annual aggregate claims for employer liability risks.
Year
5
Risk
1
2
3 4 5
Yi
(Yij – Y;)²
-
1
2
3,894 5,188 3,582 4,680 5,182 4,505
3,940 2,994 3,582 4,068 4,434 3,804
3 4,382 5,028 4,434 4,844 5,642 4,866
2,180,690
1,190,476
1,049,784
(a) Using Model 1 of empirical Bayes credibility, calculate the credi-
bility factor and credibility premium for next year for each of the
three risks.
190
NO CLAIM DISCOUNTING IN MOTOR INSURANCE
(b) Suppose now that you also have a risk volume denoted Pij corre-
sponding to each Yij above. Some summary statistics for the risk
volumes are as follows:
5
Risk
Pij
1
1
3,560
2
2,276
3
4,012
In using Model 2 for empirical Bayes credibility theory, the credi-
bility premium per unit of risk volume for next year for risk 1 has
been calculated to be 6.46. Calculate the credibility premium per
unit of risk volume for next year for risks 2 and 3.
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