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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 Yi, denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 45 Y₁ Σ(Y-Y)² 1 1 2 3 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 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 ΣPij 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 Yi, denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 45 Y₁ Σ(Y-Y)² 1 1 2 3 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 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 ΣPij 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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 Yi, denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 45 Y₁ Σ(Y-Y)² 1 1 2 3 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 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 ΣPij 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.
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 Yi, denotes claims in year j for risk i. TABLE 5.13 Annual aggregate claims for employer liability risks. Year 5 Risk 1 2 3 45 Y₁ Σ(Y-Y)² 1 1 2 3 3,894 5,188 3,582 4,680 5,182 4,505 3,940 2,994 3,582 4,068 4,434 3,804 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 ΣPij 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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