Table 46 BuhlmannStraubs Premiums ˆ Z j 09847 09276 08985 07279 09588 ˆ M a j

# Table 46 buhlmannstraubs premiums ˆ z j 09847 09276

• 15

This preview shows page 14 - 15 out of 15 pages.

Table 4.6: B¨uhlmann–Straub’s Premiums ˆ Z j 0.9847 0.9276 0.8985 0.7279 0.9588 ˆ M a j 2,055 1,524 1,793 1,443 1,603 The estimated parameters used in the above premiums are: (1) the collective premium for the whole portfolio, ¯ X ˆ ZW = \$1 , 684, (2) the estimated within–class variance ˆ s 2 = 1 . 39 × 10 8 , (3) the estimated between–class variance (of conditional means) ˆ a = 89 , 639. The use of weights has a significant impact on these estimates. In Class 4, which has lowest credibility (see ˆ Z 4 ) the empirical credibility premium of \$1,443 is substantially higher than the individual weighted average ¯ X 4 W of \$1,353. Its low credibility is pushing this class premium towards the portfolio average. To a large extent this is due to the fact that, on average, only 2.4% of the portfolio drivers (i.e. claims) belong to Class 4. Finally, if we compare the premiums obtained previously with B¨uhlmann’s model to these B¨uhlmann–Straub’s premiums, we have: Note that under B: ¯ X = \$1 , 671, ˆ s 2 = 46 , 000, and ˆ a = 72 , 300, while under the B–S model: ¯ X ˆ ZW = \$1 , 684 (but ¯ X WW = 1 , 865), ˆ s 2 = 1 . 39 × 10 8 , and ˆ a = 89 , 639. We shall compare the estimates obtained with the above data to those produced with different models studied in the next few chapters.

Subscribe to view the full document.

4.2. THE B ¨ UHLMANN–STRAUB MODEL 49 Table 4.7: B¨uhlmann’s vs B¨uhlmann–Straub’s Premiums B¨uhlmann’s model ˆ Z 0.9496 0.9496 0.9496 0.9496 0.9496 ˆ M a j ( B ) 2,044 1,519 1,814 1,376 1,602 B¨uhlmann–Straub’s model ˆ Z j 0.9847 0.9276 0.8985 0.7279 0.9588 ˆ M a j ( B - S ) 2,055 1,524 1,793 1,443 1,603
• Fall '09
• Dr.D.Dryanov
• Trigraph, Estimation theory, Mean squared error, Bias of an estimator, Credibility Models

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes