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18 VaR mean ) VaR mean (Z.) ratio (a) (b) (c)=(b)/(a) 1% % % % % % % % % % % % % % % % % % % %
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21 Development triangle CoVa claim amounts in motor liability AY/DY mean 10.8
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25 year earned premiums 444' ' ' ' ' ' ' ' ' '291 adjusted for business cycle 470' ' ' ' ' ' ' ' ' '291 number of risks 606' ' ' ' ' ' ' ' ' '263 number of claims claim frequency 10.6% 11.6% 11.2% 11.2% 10.8% 10.9% 10.6% 10.5% 10.3% 10.3% total claim amount 443' ' ' ' ' ' ' ' ' '176 claims average 6'927 7'061 7'357 7'311 7'322 7'792 7'563 7'182 7'819 7'707 adjusted for trends 7'996 8'013 8'210 8'027 7'909 8'284 7'916 7'402 7'937 7'707 loss ratio 443' ' ' ' ' ' ' ' ' '176 observed 100.1% 99.7% 99.1% 102.5% 106.7% 113.7% 118.0% 122.8% 125.7% 125.6% with adjusted premiums 106.1% 111.1% 112.7% 119.2% 119.6% 122.4% 122.1% 122.7% 124.7% 125.6%
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30 development triangle cumulative payments dev. year acc. year Ultimate '670 5'817 6'462 6'671 6'775 7'002 7'034 7'096 7'204 7'326 7'395 7'438 7'468 7'541 7'580 7'677 7'794 7'919 8'047 8'051 8'152 8' '827 7'600 8'274 8'412 9'059 9'197 9'230 9'277 9'331 9'435 9'864 9'621 9'654 9'704 9'743 9'745 9'745 9'748 9'749 9'749 9'749 9' '130 10'852 11'422 12'024 12'320 12'346 12'379 12'426 12'460 12'500 12'508 12'547 12'557 12'624 12'639 12'644 12'647 12'666 12'711 12'713 13'063 13' '244 13'340 13'758 13'853 13'894 13'942 13'980 14'001 14'012 14'070 14'085 14'098 14'111 14'118 14'120 14'133 14'141 14'145 14'166 14'167 14'167 14' '019 14'223 15'403 15'579 15'732 15'921 16'187 16'420 16'531 16'559 16'568 16'585 16'597 16'614 16'617 16'619 16'681 16'681 16'687 16'711 16'748 16' '966 14'599 15'181 15'431 15'506 15'538 15'906 16'014 16'537 16'833 16'951 17'038 17'040 17'195 17'298 17'307 17'308 17'308 17'309 17'310 17'311 17' '441 15'043 15'577 15'784 15'926 16'054 16'087 16'107 16'311 16'366 16'396 16'414 16'419 16'426 16'480 16'480 16'480 16'480 16'482 16'482 16'482 16' '578 15'657 16'352 16'714 17'048 17'289 17'632 17'646 17'662 17'678 17'693 17'700 17'706 17'706 17'712 17'713 17'718 17'719 17'719 17'719 17'719 17' '214 16'482 17'197 17'518 18'345 18'480 18'505 18'520 18'578 18'633 18'671 18'689 18'746 18'772 18'774 18'804 18'804 18'804 18'806 18'806 18'809 18' '442 17'621 18'465 18'693 18'882 18'965 20'464 20'522 20'558 20'607 20'611 21'250 21'257 22'505 22'509 22'516 22'518 22'522 22'523 22'527 22'611 22' '720 17'779 18'655 18'940 19'098 19'368 19'970 20'162 20'195 20'415 20'510 20'594 20'657 20'752 20'823 20'899 20'983 21'124 21'622 21'627 21'708 21' '293 20'689 21'696 22'439 22'798 23'054 23'394 23'554 23'888 24'061 24'096 24'301 24'356 24'389 24'391 24'784 24'784 24'794 24'894 24'900 24'993 24' '063 22'917 23'543 24'032 24'156 24'232 24'360 24'410 24'884 24'896 24'968 25'031 25'172 25'459 25'460 25'470 25'734 25'774 25'877 25'883 25'980 25' '986 23'958 25'090 25'392 25'546 26'099 26'129 26'149 26'166 26'231 26'328 26'743 27'023 27'048 27'075 27'168 27'234 27'276 27'386 27'392 27'494 27' '681 24'867 25'871 26'463 26'941 27'120 27'164 27'183 27'250 27'490 27'497 27'561 27'565 27'582 27'706 27'787 27'855 27'898 28'010 28'017 28'121 28' '595 25'152 26'140 27'090 27'568 27'637 27'805 28'003 28'223 28'240 28'245 28'250 28'257 28'297 28'347 28'430 28'499 28'543 28'658 28'665 28'772 28' '547 25'396 26'506 27'043 27'866 27'882 27'903 27'933 28'492 28'545 28'564 28'686 28'695 28'897 28'948 29'033 29'104 29'149 29'266 29'273 29'382 29' '449 22'702 23'909 24'690 26'083 26'525 26'567 26'640 26'695 26'801 26'814 27'018 27'078 27'269 27'317 27'397 27'463 27'506 27'616 27'623 27'726 27' '043 26'918 28'256 28'569 28'964 29'268 29'344 29'393 30'159 30'936 30'966 31'122 31'190 31'410 31'466 31'558 31'635 31'684 31'811 31'819 31'937 31' '655 26'241 27'369 28'063 28'346 28'780 29'024 29'180 29'250 29'575 29'660 29'809 29'875 30'085 30'138 30'227 30'300 30'347 30'469 30'476 30'590 30' '789 25'547 27'099 27'801 27'919 28'052 30'020 30'035 30'456 30'663 30'750 30'905 30'973 31'192 31'247 31'338 31'415 31'463 31'590 31'597 31'715 31' '538 23'830 25'202 26'462 27'056 27'480 27'564 27'612 27'873 28'062 28'143 28'284 28'347 28'546 28'597 28'681 28'751 28'795 28'911 28'917 29'025 29' '113 23'405 26'822 27'711 28'080 29'203 29'647 29'751 30'032 30'236 30'323 30'475 30'542 30'758 30'812 30'903 30'978 31'025 31'150 31'157 31'274 31' '543 22'674 23'603 24'159 24'242 24'425 24'767 24'854 25'089 25'260 25'332 25'459 25'515 25'695 25'741 25'816 25'879 25'919 26'023 26'029 26'126 26' '590 22'337 23'442 24'031 24'665 24'942 25'292 25'380 25'621 25'794 25'868 25'998 26'056 26'239 26'286 26'363 26'427 26'468 26'574 26'580 26'680 26' '976 21'527 22'615 23'242 23'653 23'918 24'254 24'339 24'569 24'736 24'806 24'931 24'986 25'162 25'207 25'281 25'342 25'381 25'483 25'489 25'585 25' '932 20'118 21'309 21'824 22'209 22'459 22'774 22'853 23'070 23'226 23'293 23'410 23'462 23'627 23'669 23'738 23'796 23'832 23'928 23'934 24'023 24' '538 20'357 21'435 21'953 22'341 22'592 22'909 22'989 23'206 23'364 23'431 23'548 23'600 23'767 23'809 23'879 23'937 23'974 24'070 24'076 24'166 24' '888 19'413 20'441 20'935 21'304 21'544 21'846 21'922 22'130 22'280 22'344 22'456 22'506 22'664 22'704 22'771 22'826 22'861 22'953 22'959 23'045 23' '153 ultimate (Mack) one year sqrt sqrt acc. year Cl-Reserve CoVa mse Vko_CDRi mse % % % % % % % % % % % % % % % % % % % % ' % % ' % % ' % % ' % % ' % % ' % % ' % % ' % % ' % 1' % ' % 1' % 801 Total 32' % 4' % 2'131
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33 lob description 1 motor liability 2 motor hull 3 property 4 general liability 5 workers compensation (UVG) 6 corporate accident without UVG 7 corporate health 8 individual health 9 marine 10 aviation 11 credit and surety 12 legal protection 13 others standard default parameters for CY- risks lob par CoVa (claim size) % % % % % % % % % % % % % 5.00 standard default parameters for PY-risks lob par fluct 1 3.5% 2.5% 2 3.5% 20.0% 3 3.0% 15.0% 4 3.5% 4.0% 5 2.0% 4.0% 6 3.0% 5.0% 7 3.0% 7.0% 8 5.0% 0.0% 9 5.0% 25.0% % 20.0% % 15.0% % 0.0% % 50.0%
34 Correlation matrix for CY-year risks lob big claims CY lob Pareto parameter
35 lob description 1 motor, third party liability 2 motor, other classes 3 marine, aviation & transport (MAT) 4 fire and other damage to property 5 third-party liability 6 credit and suretyship 7 legal expenses 8 assistance 9 miscellaneous non-life insurance 10 NP reins property 11 NP reins casualty 12 NP reins MAT
36 lob standard parameters CY-risk (premium) PY-risk (reserve) max historical years m n 1 9% 12% % 7% % 10% % 10% % 15% % 15% % 10% 5 8 8% 10% % 10% % 15% % 15% % 15% 10 credibility weights i for 2 historical years available m n correlation matrix for Z-variables (combined premium and reserve risk) lob
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Property and casualty insurance business in Switzerland
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