PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

More documents

Recommendations

Info

468 A NEW METHOD OF ESTIMATING LOSS RESERVESwhich leads to the first estimate of the total incurred for accidentyear i given the incurred losses through development year j:Ŝ (1) C iji= P jr=0 E[Y (N+1¡r) ] (12)i.e., the loss development factor from j to ultimate isLDF (1)j,N = 1P jr=0 E[Y (N+1¡r)](13)for j =0,1,:::,N. Alternatively, we may use"#Ŝ (2)1i= C ij E P jr=0 Y (N+1¡r)(14)which yields the alternative loss development factor from j toultimate"#LDF (2)j,N = E 1P jr=0 Y : (<strong>15</strong>)(N+1¡r)From Jensen’s inequality, LDF (2)j,N ¸ LDF(1) j,Nfor every j. Beforecalculating the values of LDF (1)j,Nand LDF(2)j,Nfor various valuesof j and N, the distribution of the Y (j) ’s will be provided.From the theory of the random division of an interval of unitlength (for example, David [6, chapter 5.4] or Feller [9, chapter1]), the variables Y 1 ,Y 2 ,:::,Y N+1 form an exchangeablesequence of dependent random variables with joint pdf:f(y 1 ,y 2 ,:::,y N+1 )8>< (N +1)! if y j ¸ 0 and=>:0 otherwise:N+1 Xk=1y k =1:
A NEW METHOD OF ESTIMATING LOSS RESERVES 469The marginal distribution of Y (j) is given by Maurer and Margolin[12, equation (4.4)] asÃ !N+1 Xm ¡ 1Pr[Y (j) >y]= (¡1) m¡(N+2¡j)m=N+2¡jN +1¡ jÃ !½N +1£ (1 ¡ my) N I y< 1 ¾mmwhere IfAg is an indicator of the occurrence of the event A. Inaddition, the moments of Y (j) satisfy the recursion(n ¡ j)¹ (k)j:n + j¹(k) j+1:n = n¹(k) j:n¡1(<strong>16</strong>)where ¹ (k)j:n = E[Yk (j)] for sample size n.Due to the difficulties in deriving the inverse moments neededin LDF (2)j,N , however, Monte Carlo simulations6 areusedtodetermineboth sets of loss development factors. Table A1 in the Appendixshows the loss development factors LDF (1)j,Nand LDF(2)j,N ,respectively.4. NUMERICAL EXAMPLESExample 1: A Simple Data SetSuppose a new product was introduced on January 1, 2000and the loss development data as of December 31, 2002 are givenin Table 2.The total paid loss to date is thus 1,719 + 2,573 + 1,761 =6,053. To estimate the total ultimate loss, we must first specifyN. If we assume N = 3, then the total estimated ultimate loss for6 The uniform (0,1) random number generator run in Press et al. [13, chapter B7, page1142] is used to perform all simulations.
Page 1 and 2:
VOLUME XCII NUMBERS 176 and 177PROC
Page 3 and 4:
FOREWORDActuarial science originate
Page 5 and 6:
2005 PROCEEDINGSCONTENTS OF VOLUME
Page 7 and 8:
2005 PROCEEDINGSCONTENTS OF VOLUME
Page 9:
Editorial Committee, Proceedings Ed
Page 12 and 13:
2 AN EXAMINATION OF THE INFLUENCE O
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
10 AN EXAMINATION OF THE INFLUENCE
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 39 and 40:
AN EXAMINATION OF THE INFLUENCE OF
Page 41 and 42:
RISKINESS LEVERAGE MODELSRODNEY KRE
Page 43 and 44:
RISKINESS LEVERAGE MODELS 33There a
Page 45 and 46:
RISKINESS LEVERAGE MODELS 35where f
Page 47 and 48:
RISKINESS LEVERAGE MODELS 37where a
Page 49 and 50:
RISKINESS LEVERAGE MODELS 39Various
Page 51 and 52:
RISKINESS LEVERAGE MODELS 41Then, f
Page 53 and 54:
RISKINESS LEVERAGE MODELS 43This fo
Page 55 and 56:
RISKINESS LEVERAGE MODELS 45This ri
Page 57 and 58:
RISKINESS LEVERAGE MODELS 47differe
Page 59 and 60:
RISKINESS LEVERAGE MODELS 49The las
Page 61 and 62:
RISKINESS LEVERAGE MODELS 51ple. Th
Page 63 and 64:
RISKINESS LEVERAGE MODELS 53the TVA
Page 65 and 66:
RISKINESS LEVERAGE MODELS 55We also
Page 67 and 68:
RISKINESS LEVERAGE MODELS 57Mean Va
Page 69 and 70:
RISKINESS LEVERAGE MODELS 59APPENDI
Page 71 and 72:
DISCUSSION OF A PAPER PRESENTED AT
Page 73 and 74:
RISKINESS LEVERAGE MODELS 63known t
Page 75 and 76:
RISKINESS LEVERAGE MODELS 65to be a
Page 77 and 78:
RISKINESS LEVERAGE MODELS 67implies
Page 79 and 80:
RISKINESS LEVERAGE MODELS 69bad res
Page 81 and 82:
RISKINESS LEVERAGE MODELS 71a maxim
Page 83 and 84:
RISKINESS LEVERAGE MODELS 734. INTE
Page 85 and 86:
RISKINESS LEVERAGE MODELS 75the two
Page 87 and 88:
RISKINESS LEVERAGE MODELS 77that a
Page 89 and 90:
RISKINESS LEVERAGE MODELS 79REFEREN
Page 91 and 92:
RISKINESS LEVERAGE MODELS 81EXHIBIT
Page 93 and 94:
RISKINESS LEVERAGE MODELS 83
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
WHY LARGER RISKS HAVE SMALLER INSUR
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
ADDRESS TO NEW MEMBERS 151ateship a
Page 163 and 164:
ADDRESS TO NEW MEMBERS 153You shoul
Page 165 and 166:
ADDRESS TO NEW MEMBERS 155strength
Page 167 and 168:
MINUTES OF THE 2005 CAS SPRING MEET
Page 169 and 170:
MINUTES OF THE 2005 SPRING MEETING
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Volume XCII, Part 2 No. 177PROCEEDI
Page 189 and 190:
MODELING FINANCIAL SCENARIOS 179Bab
Page 191 and 192:
MODELING FINANCIAL SCENARIOS 181tur
Page 193 and 194:
MODELING FINANCIAL SCENARIOS 183the
Page 195 and 196:
MODELING FINANCIAL SCENARIOS 185Ho
Page 197 and 198:
MODELING FINANCIAL SCENARIOS 187rat
Page 199 and 200:
MODELING FINANCIAL SCENARIOS 189sto
Page 201 and 202:
MODELING FINANCIAL SCENARIOS 191the
Page 203 and 204:
MODELING FINANCIAL SCENARIOS 193Dyn
Page 205 and 206:
MODELING FINANCIAL SCENARIOS 195(ht
Page 207 and 208:
MODELING FINANCIAL SCENARIOS 197In
Page 209 and 210:
MODELING FINANCIAL SCENARIOS 199equ
Page 211 and 212:
MODELING FINANCIAL SCENARIOS 201neg
Page 213 and 214:
MODELING FINANCIAL SCENARIOS 203ide
Page 215 and 216:
MODELING FINANCIAL SCENARIOS 205tra
Page 217 and 218:
MODELING FINANCIAL SCENARIOS 207mod
Page 219 and 220:
MODELING FINANCIAL SCENARIOS 209TAB
Page 221 and 222:
MODELING FINANCIAL SCENARIOS 211mak
Page 223 and 224:
MODELING FINANCIAL SCENARIOS 213FIG
Page 225 and 226:
MODELING FINANCIAL SCENARIOS 215str
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
MODELING FINANCIAL SCENARIOS 223are
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
MODELING FINANCIAL SCENARIOS 231
Page 243 and 244:
MODELING FINANCIAL SCENARIOS 233ete
Page 245 and 246:
MODELING FINANCIAL SCENARIOS 235[10
Page 247 and 248:
MODELING FINANCIAL SCENARIOS 237[30
Page 249 and 250:
WHEN CAN ACCIDENT YEARS BE REGARDED
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
THE APPLICATION OF FUNDAMENTAL VALU
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428: THE APPLICATION OF FUNDAMENTAL VALU
Page 473 and 474: A NEW METHOD OF ESTIMATING LOSS RES
Page 477: A NEW METHOD OF ESTIMATING LOSS RES
Page 497 and 498: ARCHITECTURE FOR RESIDENTIAL PROPER
Page 529 and 530:
ARCHITECTURE FOR RESIDENTIAL PROPER
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
Page 541 and 542:
Page 543 and 544:
Page 545 and 546:
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
Page 553 and 554:
Page 555 and 556:
Page 557 and 558:
Page 559 and 560:
Page 561 and 562:
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
Page 581 and 582:
Page 583 and 584:
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
ESTIMATING THE WORKERS COMPENSATION
Page 591 and 592:
Page 593 and 594:
Page 595 and 596:
Page 597 and 598:
Page 599 and 600:
Page 601 and 602:
Page 603 and 604:
Page 605 and 606:
Page 607 and 608:
Page 609 and 610:
Page 611 and 612:
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
Page 625 and 626:
Page 627 and 628:
Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
Page 635 and 636:
Page 637 and 638:
Page 639 and 640:
Page 641 and 642:
Page 643 and 644:
Page 645 and 646:
Page 647 and 648:
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
Page 663 and 664:
Page 665 and 666:
Page 667 and 668:
Page 669 and 670:
Page 671 and 672:
Page 673 and 674:
Page 675 and 676:
Page 677 and 678:
Page 679 and 680:
Page 681 and 682:
Page 683 and 684:
Page 685 and 686:
Page 687 and 688:
Page 689 and 690:
INCORPORATION OF FIXED EXPENSESGEOF
Page 691 and 692:
INCORPORATION OF FIXED EXPENSES 681
Page 693 and 694:
Page 695 and 696:
Page 697 and 698:
Page 699 and 700:
Page 701 and 702:
Page 703 and 704:
Page 705 and 706:
Page 707 and 708:
Page 709 and 710:
Page 711 and 712:
Page 713 and 714:
Page 715 and 716:
Page 717 and 718:
Page 719 and 720:
Page 721 and 722:
Page 723 and 724:
Page 725 and 726:
Page 727 and 728:
DISCUSSION OF PAPER PUBLISHED INVOL
Page 729 and 730:
APPLICATION OF THE OPTION MARKET PA
Page 731 and 732:
Page 733 and 734:
Page 735 and 736:
Page 737 and 738:
Page 739 and 740:
Page 741 and 742:
Page 743 and 744:
Page 745 and 746:
THE “MODIFIED BORNHUETTER-FERGUSO
Page 747 and 748:
Page 749 and 750:
Page 751 and 752:
ADDRESS TO NEW MEMBERS-NOVEMBER 14,
Page 753 and 754:
ADDRESS TO NEW MEMBERS 743Now to an
Page 755 and 756:
PRESIDENTIAL ADDRESS-NOVEMBER 14, 2
Page 757 and 758:
PRESIDENTIAL ADDRESS 747use of thes
Page 759 and 760:
PRESIDENTIAL ADDRESS 749just lookin
Page 761 and 762:
PRESIDENTIAL ADDRESS 751The quantif
Page 763 and 764:
PRESIDENTIAL ADDRESS 753me keep my
Page 765 and 766:
MINUTES OF THE 2005 CAS ANNUAL MEET
Page 767 and 768:
MINUTES OF THE 2005 ANNUAL MEETING
Page 769 and 770:
Page 771 and 772:
Page 773 and 774:
Page 775 and 776:
Page 777 and 778:
Page 779 and 780:
Page 781 and 782:
Page 783 and 784:
Page 785 and 786:
Page 787 and 788:
Page 789 and 790:
Page 791 and 792:
REPORT OF THE VICE PRESIDENT—ADMI
Page 793 and 794:
Page 795 and 796:
Page 797 and 798:
Page 799 and 800:
REPORT OF THE VICE PRESIDENT-ADMINI
Page 801 and 802:
2005 EXAMINATIONS—SUCCESSFUL CAND
Page 803 and 804:
Page 805 and 806:
Page 807 and 808:
Page 809 and 810:
Page 811 and 812:
Page 813 and 814:
Page 815 and 816:
Page 817 and 818:
Page 819 and 820:
Page 821 and 822:
Page 823 and 824:
Page 825 and 826:
Page 827 and 828:
Page 829 and 830:
Page 831 and 832:
Page 833 and 834:
OBITUARIESROBERT GRANT ESPIECLYDE H
Page 835 and 836:
OBITUARIES 825SIDNEY M. HAMMER1931
Page 837 and 838:
OBITUARIES 827J. GARY LaROSE1947—
Page 839 and 840:
OBITUARIES 829PAUL J. SCHEEL SR.193
Page 841 and 842:
OBITUARIES 831LEO M. STANKUSCirca 1
Page 843 and 844:
INDEX TO VOLUME XCIIPage2005 EXAMIN
Page 845 and 846:
835GRAVES, CLYDE H.INDEX—CONTINUE
Page 847 and 848:
837INDEX—CONTINUEDREPORT OF THE V
show all

PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

Create successful ePaper yourself

Delete template?

Save as template?