ࡱ> `!b=?,99L6.D0xJ`.6i0 P:袅q `8VX1Ђd8Nn}'xwb‘]|k O'ɖ8Q+HykZi:M*g[l@.M9{2{SjB8L.M iFx8ogdž:5vD"2繥c|WGpjѼ }pC,:4]^[(|dܮ g |0u,]H1"}6ެ@Pn -AJW$j$N ]<_P`!؞@=y!u>-tj  ȽXJoxcdd``c!0 ĜL0##0KQ*faR`R` A?d-@1FnĒʂT.(X'#M`[`!> g2R>@HGa\xQJP=wRU HA . |u%.J@ҋVMdWW.\q!.mx$79sfNf#3J: !"(2u(؋dt5VΪʚ ȴuS=vOKi N 'xe3`zo=Y}]]GyjBQ>ҶbVIQ@N(={S+/Tz -[e dd8w9̼e0rm/? IJG]'w?~/ta=Tĉ{8|3nwQ^ʂh_Rˌq ,hD`\xKK1'Vh}'RU ŋ'OT,U[ފݏPAуG?A<ЖI+e.䟙_f #Bց4DC z.gfـ!sueOwQ-CP'B?r ;>O@YzV0R=ᖾ(V>9Q͈Y|59L1\'>WewW k_ů 3Q?$BM|0K{3N`LN4M:J۾ʮ2)f2dOe63A+3FH{i#wFLď{MzLYr;w/7|R|3@yPwO5.Փibx+ͥpڸ'.@`!}jþ6d6o萻ndod %wKxcdd``6bd``beV dX,XĐ iW A?db /.ĒʂT& ~35;a#L ! ~ Ay L 9qb8o PH>? PkxA|C8?,7o>#f #`' > #d13ĥaI9 ,H-ܥM ~gJ`y]|<D=4  `p321)W2_O`!MԚ/Lղ@x$H x=K@ǟƼԤPJ.Iꠂ-+VhdI Ă8u N]$NS.טTK7B14h4Ax:i6bգ'"$IP[o;>q;8[iɹ:_r;&{r>+A~S]RIH^/Hz%(ṕʦq<gcg#J7f}/|z~XvsUzIGOأ/{аModRr=m$9?S_IAiZ|wGEB_1X)&# lNZø#R*@ALf[ṶWq\"SQZOy#v2{牗5mm%~d9YëgkGkwC-i[0(ow @8.[ av-_@TGJxG+_({elH|. Ϥ|/I"{|OcGwR[LySdϘJ_?M?mYvml|9WS!f[fՃZF a`!3ǦNy@&Otq@s`PxSAk@~nmѴ BUZY*"T[]=5̺)ɒ\J鱇"< zzŋ"뼗h*bB|ooLxy&V 88rC\<=6o 7KٌY]m0$ >2O29#3Yq`%{bO6@Q2vZz7agVaɖ]cG.d*ϛwz*Us̱'ԥB4TCDҹtܧI*غWwx|Ro>/rO^*xzҞ}B Vf.Rf^jIr˗(t4j ol_WM6S8[<U.˩9VS#?4R{;^$󈤼Җ^ivKEiE"ݓ%.a}z*}ړǼ_ew `! jfFAWCd5* 3`AO`\xK1߼9Z+Rg 8(.N~ Z\bj MwAJG7U N.ԼIXꛡdQRalwqc\"!T2\L3D (FMn#E7yxWOW3+9^c%Ռƥ]~cnJ <,yGsYE~ꋜvGLIC[ ٓQ~ۋaSaT wYSl'w8WnPw[#r^pI7C[gskĥ &`!bV,]Fn"[w\4 &w0xcdd``bd``beV dX,XĐ i A?d< ^\@=P5< %! L fz `W01d++&1(] F\ T^(j<Gʕ H$ǩIiyi GLDǬf.#ai9Yѳww>e~WaYZ_wkoxs.2nWRRDFSIj0~ׅ~'Sc?5EIgS"nE ~;y]9rC|:_Az:9W5jW6q?f%U /ZW q&ƥ7p.8T>3)?PqW+Q>YeȇKޛސZ!ac?J.5xQO=6!R;^ȁO?*[(lW$?hA(5^\3r?QZ'J_K) ]5P;&b1{E,;]3\?x5kP9F^yM'1~{*_e3.tʳ҅\50_!蝀eʕ=X/'cMkcӟ5'e|6@#ez2US~ol_f6A}ƙcTq/M >T7C=n!,Qb'@S1sKnyGn}:QEetV7VAj؂锜o3z;m~R؉ZÉph#W70ɭw_y^®Ҿˢ?;'q%c}`|Q%?+ٛ{7+/âyKlZv{;[ajYq̸w2@ZiD{(L!;ߓ!ol `E`!'P5M2, 'n=pxK1_rkz jEܜ7E nV(?ܦC'.$".@p+Rrט!$%߼B x ?S&h9ChV3CΌQ[7ӺE+`0 ]PC'߈@ Ƃtqm)d *_Rl2;|6)$)âgA4^W׏<8G)FP|Չ$D@9@, fbd02,(1dbfab~ 'd3H1ibYkxnĒʂTLXf"P 27)?"](6r`i)` N#_\T .%M _0129$ j#Զ3p$BpH9 Ʊ><1C1Jh@)9?nR[{Up,ua@Q >Xa G  `pĤ\Y\ːG`uұ`!0"*M,x@ %(xJA^+ƐHxˆF x$j0D,KX [YX6F,$uٙog =11-qL8$9]Sgsr1J=0 AX'FHqmKhd ә\XY牷-L Gr~ӯh\EnhC:Fc~CG 彾IUlX>%s_T>UVVv,T>$5gEr!X= dOs4q~yb.Z:JRt[s;3l䠷CѺjyLq7s}FNJֻ*2}+`(kT+j "O}y#o(>d_izsG9 Qr_ ѹc;Ŭ v75`͈`!^>ɇK2sXB Rtxcdd``a!0 ĜL  312Ec21BUs30)070Qcgb VP)znĒʂT.(X'#=`S`!VMG ڢy/z, 5` [R.$xMk1ǟd6XgZA;-ZZ0)UWuJ ayo~S~= H{Rc$[N~dpS wVNܔChgɞ2%Z]q>JIpR @+Mۗ "Fk|^|\\)*` ZCK#Ѹ9}e0 '#oſ/tDV~@?xȉդި> o'̛ NMHg' ]̸?\6|>l}+E[Yfv>{J*o?搻;y|_5";kgp^v% gZ4CyyY~1a/8Zk+eJߒߑ @b1##X`=F !#T57Lf5! KA?HZTzjx|K2B* R6Uf[2adBܤt@ڈˆ)^DH}`~%URM35D? PHfnj_jBP~nb &90}7+|/b6pk MYp>ȀpwaT¨{PEUgQݙP[1O3L@> Qp()Jdh@jXu`)MA|m87pPݽ2C炦i.pG-Lv0o8021)W2"%}`!>X p= ? bP&xMLACb- K0"`BzMڃ#sz`cʪ/AFc 4Jv^Tcoj`;JtXQ隦hz.Sgڴ:ӡk\]n5! 9XG7@/h|?4}x0u, ) YWvGe־YOJ4﬑&'g1_;_s"ؿX~Mņۚ%&ؿX~mUE5|(GS]Cc\'b,!N%\KUG\f֑|;p>!0pфj)¼׷%?iG877X{r~+H;wM;Q=oIgEO<+ hB;՟k-x$MTdzy՛Tk%Q}8LCDCOhd)g-.)v4A7~2|f- _WOexn57?i?i ڙzou?jp&M6WE_k2گh&}&ŚR.ߌxn [d|E+|[U ]ٮrA`W!ǍT]WRS8"߅樂/zJѭGro'ܕJ|=Sd|]^2I{c)3keZ`z?RNLO?:x0iIUSn~Ou8<E՛(rtMF`! 1Ma4V  CJoxcdd``c!0 ĜL0##0KQ*faR`R` A?d-@1FnĒʂT.(X'#M`[`!NXhȍM,RcC@4Q:xKLQyVA! "I10q.!$F:5eA*BY%1pc%KC\21iXҐA` Թ{P4N?;#! ![FHFy_ddO",ItF¹\KtK\m8'~{T#Ags{t{ۦfl5&I\v-hrTЌus߇gGRK\}Wɔ39_2f%h?X i?_w"60:9]lr~<r `ީ[ΝOՄ8.P^6ڎ"o|Z*C3V^u ʐ{5k7 %ϒ,/W2E~/Յٺnv󺳾[܁cDZ9=.a'Þ*C/i$"F0I?3/Hi,翙D? PHfnj_jBP~nb,&=`Ti20ryp{._3,3XPcK5qy HS$ Jh5Q}| Ta]1N`B`` #RpeqIj.CG]Q`!]ղN\@ H1 x/A߼sֹh\B)*KݑKH' :QVPPttJ5̛ fw3{vA|@B y#cjaZU3C,f2Ȍ:(>6@T[9"JHih0UZl6FK=Q^l]Z_ F]$};SϿJ_Oh7ԕc#RU888w*Λ֪h dUXN۩uP^|7Җ=Ahy4H"=J ZpH&7-g,OĉK=^vz6?j5md*vn!yçxx0?sAA5-OZ%Ꟙ޹|odcI-O'l[=~ޤ߇ ӫ irp Fw3[)o](ה+tP`!#1Ĭ U(vW:`- WFFxKhAgfg1X`KP,:_d>Ο7zrJp|Qr0匬>9u.;z8wztb]=Q]ω jy2O9_/_տb- Ii@Ğԛr%w2w=Ph^ž wJ=+{k\C4"xx00C*X\_7)=[PWάfO *弜j' |*7o;VUWWO܌lE~LD~Ͱ_C>#~ `) =g_ P|RZ@qtJB`!hCcpYEAY Jv )wxSKA~v?@A]"҃BD=tܥ? EݺtIffaРYf}off xB_6tzY:HܳJܓE"8obZN?aH`R<8A9"ۥa:)"fbg_}GìyjU&wg=_TˍN4Wj wal <:!3KJK`+x)?нc#(i# W1U=Q=! /S:A5_K3\Q_/CwvЎ7gw cA{ߊ׻.[dd=)ٻyK| qg ~A \? &sVYBm'isog( a  0Equation Equation.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00B Equation Equation.30,Microsoft Equation 3.00L$Equation Equation.30,Microsoft Equation 3.00Q%Equation Equation.30,Microsoft Equation 3.00^&Equation Equation.30,Microsoft Equation 3.00f'Equation Equation.30,Microsoft Equation 3.00j(Equation Equation.30,Microsoft Equation 3.00k)Equation Equation.30,Microsoft Equation 3.0D0l*Equation Equation.30,Microsoft Equation 3.00m+Equation Equation.30,Microsoft Equation 3.00o-Equation Equation.30,Microsoft Equation 3.00/Equation Equation.30,Microsoft Equation 3.00:%Equation Equation.30,Microsoft Equation 3.00<&Equation Equation.30,Microsoft Equation 3.00='Equation Equation.30,Microsoft Equation 3.00>(Equation Equation.30,Microsoft Equation 3.00@)Equation Equation.30,Microsoft Equation 3.00B*Equation Equation.30,Microsoft Equation 3.0<0C+Equation Equation.30,Microsoft Equation 3.0\0D-Equation Equation.30,Microsoft Equation 3.00^.Equation Equation.30,Microsoft Equation 3.00_/Equation Equation.30,Microsoft Equation 3.00`0Equation Equation.30,Microsoft Equation 3.001c1Equation Equation.30,Microsoft Equation 3.00nf2Equation Equation.30,Microsoft Equation 3.00g3Equation Equation.30,Microsoft Equation 3.0B .Clrs9809_2_appendix.ppt095 Equation.30,Microsoft Equation 3.00W6Equation Equation.30,Microsoft Equation 3.00X7Equation Equation.30,Microsoft Equation 3.0/ 0DTimes New Roman|d 0 & 0 DWingdingsRoman|d 0 & 0  DSymbolgsRoman|d 0 & 0  ` .  @n?" dd@  @@``_`7L7CARBRAKE.WAV.WAV 101026RIFF6WAVEfmt ++data6~~~~~~~~~~~~}}}}}}}{{}}}}}~~~~~~~}{{{{{{{{{}}}{{{}~}}{}}~}}}}}~~~~}}}{yxvvuusqqppnnlnnppqsssuvvuvvxxxy{{{{}~~~~}}{{{{{~~~~~}{xxyuvxy~~}}y~~~}}{~~}y}xxuxuvvvvx{yy}yyy}~~~~~yy}xvvy}sps{{qiksuqgiqsqnlqusnpsx{{{{{yy{yxqquupnglpqpnpqsusu}}xxyy{{{~}}xxyxvqpqvunnqussssssqquusvx{~~{{}{usqkipniggkpvspsvuy{xxyy{yxy}~yx{{y}}~~{uvvvxunkqunlnpquxvy}}}vvvspnklkiilpquuvxyy{yuuqppnnquvxxuvvx}~{~}}}}{xxvpknpppuuqsslinqsusssxxyx{{vqppkilngablvupq{~{y}}vyuuqlkknpnkilllklpqplnsyy{}~}~~}xuuqqnqplfffffliklsxxxxx~~~~~~{uquupigkppu{}~~~}~}}{y{~vuvqqssv~}{~}xsspifdddfkpsv{~}xuuusuuuusvxvvxy}~~yuqifdddbaabfa^_abadfflkklsxvx~~~}}{yyvuvvvyyvvx{xyslgbgb_d_bilqy~~}{sv~}{x~~}vqqux{yxx~~}~~y}qx}sxx}yussx{{vxvupgdfkd__^ZZaa_aaZZ\W_bgbbgillns{{}y~ygabi\TTOPGGJKH=CC;CMJ>@HO^^_nqv~{{vvysnklqnfgpvniv{ulnspspgfnvqgilxyupquyysllpnklqvspsyyv{}~~xx~xxuq}qgkpxskkpqlillniggglibb_bfipppuy~~}~{xsv{xvy{}}~{~}yxvvpkilpnigdgkgd__gkkkfdfinnllkpnsvusy~~y}~{}upkklklklnqslllnnkkkidadiib\_dfiiiinvuxxyxx~{xxupipnfifdggfaffgipliiiffafddglgknpv~~unkpvysx~}~~~}{y}{nglsupnsv{{{{{{{~~yx{yxqquvyxuqqy}upqnvvx~}yyvvspxypqs{yi\^^YWPJKKMTY\^Z^ipssxqpuuusuppu{up~x~uǦqx}s^HCUP=..33+"!01+)18>JOT_nsu¾}vlf_UTWRJGJMTWRORY\UUYW^a^^bilkfadluqnusv{{xpifksld_fg\RRYbdWT^inliabgkgffdkibiqvqsx}~qnxsd\lvnYTagaYPUa^WMMRMKKPTRUW\_Yaknnls~xvy}}pilppkbdbZUZ^ZWUYZ^_a\^bdknlllqyyy}vvvqifadZY\UZURUTRYU\\UTW_d_\abipsx}}{v}}xpsxqukbgl_bgnigqqnnkflvg_d_dkdZUgyndaluliianxunpx˹ǵǾqqd_UOKC90=;03>CCJRUZYUP__UTgidpx{vx}{~}xnuuҸxdRRJ9,&!  '>;=Tlvxý½yppsxgUWWYMB=BRYTC66EJKKMMRWaa\\bgldZdqx{vv{nZ^lkWKHKJCB813==9CHC>BUYPRfnkq»{vxy{l\dnliffbgfWMMR\\Y\\^TR\dbZdqplv}{nyssy}~~}{~vquyvvuqusligZPRYUKHPWYY\abkilsux~xpuupnxqqnnnpnqkdaYWWPKKORYWZ\^^iknyua\nxupv~vy~}xgiqpkddffkiinnk_fnnq^ZnyibqsvyŶxnlvpfTKO^_WY\W\^^\\\ZW\^RP^b\WYadbbd_bigdk}~^vȶxffu_E835, '+!$9MRWdxyx~Խ~sx{xnggdWPPPH@GJHKRMGMWfaKRi~xbd{~ln¹¹}~{lbpqdRKOMC86335056BJGEG^pxux~~Ŷ}~~yps}yv~~}xu{upgbdb_\Z^ZY^bdpuu~xss~}xxv}~}vupkgaWTY_YMMZddY\gsxsu~}{~xy}xqqpvxsslpslinlafffnifpx}}~qdikbZUZYa_\inffsvssllpi_\iaMKYkpgTY~basöŽ»pn{udWOR_bJ;COYYPMMKC@MKEG;BPROU\_by}pxʾn\YOB60,$ !.8EPZdyʾy~{xuqlZOOCCORMG9=JKGJKMask^^daap}ó}x{yqy}qdWKEYRJY_TJPWRPWYafdb^anlgu~}yv{x{pln_R_iliaggafffgfblqllns{vpivui_^bg_Ublfb_ipkki_bfpnggip~}xnillf\YUJJKMPU_ag_^gu~~lfu{lTRlxiUECOYE>GGHKEMMZbZds}{Ǿugpyssifvsdddf__^^ZREMYTJGC_kPMi{kks{\yҾ}ugUEEH>'$')"'55,1=HHHKM\kx~}y~skia\adUM\YYgZEM_iaKJk~y{}gZZaaZR\b_ZZaafpkZbkgddY\nvvu~vnxy~~~ndgkknkpnklxskfkvpgfggUYssgiks}x~vy{~vy~~}npuyqlnsy}sknp}{qx}~vy~xpuxvqkqpgbbgngggkpqx{~{yupqqkad\TROUUMPRT_fZOYdspiny~lWWsbMGYqkWPTUWYZTHR\\HEWfnYRuxg{°qupaWMG8+6$"+'0356BH@CMUMUpq{xy}vxu~~silZEGOYUTYOdx{}x~y~vvxq\TfdZZ\nuigkpnnqvyyuux{v{uv}}upx~sdp{xvvnyyvqik}vbsxipubv~ysy~{{uvuq}uxuux{y}x{up{~vpqspkkllnssgW^bgqpqvu{~~yniys^JGbqaP56^iH@Y^xx~~xiuuiakqxsdgnuviTYbquiWUfZYqu^Yfafyv\iäŮͳusbldTEGE55@RUWYWTfu}qadikpdYdq_dynfnuqpk\gns~{sknvya\nnfg_akd^\ik_p{}}}y½ydfs~{nUTppbYYgnlkqpiluqvqxysyxpvy{ysl}{~vysilk_glgsuiu{plpngkpnqplpkbYTbiuqs}ys}xs{qsnklYPOfsZWdlxvi{{}{}un~{slv~qysnu}}gZ}~kqn~{pnqf_Zpxvvfv~~sY_qiRPZ\da\\\Pp}{uu}pq}}pu^aqsuniy~vs}i{~q{y~{~}}nknplld_Y^gb^Zdqv}~}{}{}y~~yxxnqkq~xx~y{yxv~y~qlxqlg_ax{snki{{}xx}sy}{ylgy}}{}~xss_lpgbZbiuulpsp}}y~svyganuyp\^pvsigu~svyv{~~vplqubqvu}pdnqs~~uvq^p{~ilqyub^fvsd\\\b_PHOTHYpsl^f{sbnvv}}ifdaaiiWbqsqlku{{qx{{v}vy{vuqdknvupqxux~~~{}{qpux{vsuqqssvu{uxyx{{vx}{}}yy}{}{vxvxsvuqqkinnkkisyvv}yvxxsnnspnqsxvuux}~}}~}~~xx{}~xnnquxvppssu{}y~~xux}}yx}~}~yxy~yyxpsvxxuqs{~}yyvyvkiffgfgiiikkfilkfkpy}}y{yuuvqlgiiggkklqpqsvxysv{{xpgkqsqvvvvsspqxx{uuy{sssp}gZ_dp{us}upk^RKd}sgvk\^ny~}qdbix~fPCMfsuslbpii\M{ykYa}dvTa}^g~lGba;>UnlkKO^{kP^akv\9HfOTlqE;C=\{G^g{bGZ¬nPikPTqUs{aTUl{¸W>KaMTx>G;Kg80TpxB)KuyqdPZxǕuglp§TllE09O^uqlfG3K^Ug}ǸsPWlZCRgvö}^PW\UbpsWWYC>Kas~W=EEqff͹bn_qTHbg_M_qxT61Hfvp”RfC6U{i^~xJKk_@CZl}ùZ^}RBRfyçisZ@Jf}xծqxiCYuP6Jlg9UxuiqbJ3HgaWk¹laidsyǹvdB)!&3WZYu~}bJ95EgZWvŹqdvbGBKi}kK@RM}vnŗ{uJYqG9K\{qgT89TRMdy~pgZGEUZkԾuB1B@asWPl\=GRig\nZJpuTERk}˸nYsg@3CayybusP9CHsv{ʶnvJ{q{R>;pKsŦv9Yl_HuGRvKYOJlplvnl_dvˍWpȩlC\xvu^d}qBHOidKJi}\ulgig~{ȳpCun\~}BWuC.Ck;=ZsG8Osn{xu}pOdbORflyfYYaZ356J_lûlMbWTduxȾ—_iROHRi}Ƚ~\dC^i^Y_Uiudzd_qu;66^~k\_y~TGGkd=)9TgžԽuEpgOTp˅Z~ÙWbZ6'1JfffJ9Jb{}b;=gpunnű_g}kKP^x͵ulxiZJ;KTp{ňxqC>;~Y5JJ~guJ+ig>HCT@avԅ{¬sskPUqʾa@6=BZixŸ{~d85KaGK^vxsPEgyPZvжiO059GZZp~ylaM+$>Uk}ŤsiPaladsŬf8CKWaB;MfnqfE3=EYbp~dBETqg_sň~yf\p}as{lR;;TTMZllM'.ZYBHT}yY@W\uv϶fBOYYJ\}\Wnu}__E8Jbu}ŮRPygOfKKgyȱgU\bp^yqB58KGMbyvP;MWnYnǜU=BaaPbpYlO!)d}=MfnHGYfϧY{vM9\E\l{WniYaPa\}xM$MiEyuygȳqdH6Gqbu}xUq96TE.Rbf{Y}Zq\u~paqv_CCUnfaTi}T9HxTgg{Ȟ\dslnU{MdxgÏOWx_{iuikRk}gOWYWqsq^=8EiMps>anU9,6Zk±^^vsxnRKfy¦lMi{d\U@0JbubJqvkxb@@OWZW}s{q~\H{yUdpWMixMPOgiJsK>Zn_}yklYabZvs_ZYH\i_k{~nP6=U}}{l~dGG_yxbõu~M=Yn{pyqZaY66G\{}qiaM>Rk{NJUg}vfW@.3C^fslkgfGuWfUlx˙ͱsUa_;>Pndsg}lYWORCayvv}dOK>Rafq©ldvaREKdp~Ⱦ_ygRKH__dxld{vnqgUEgYlaagYJnu\9OTCfyf~fdf{»n_RW_Z6EEJ_p}xkG=;ffšpB+B}saZsŸ_5PlifRdyl6=yJKWky˻qU8UpPWf{¹xfO3+@TbqvxlaJ15Rnd_{öǹ^OTubxyyʳ~l\C6Kpqu\vnW.3lkZbv~ydC5T}YpqP3@Zx^pq}siG&.E^}p}«~pMRl{GWs٦\Yqf^ZfsxJ'GM_Wql{\36q~iTiʻfH1B\p\~ùg@,;TgPl{xkM,Gi\Y{axqqqfa\T^YivkWaUluagyukf~ulUKp{ZniYKbyqHRKJguxfdaUUWb~~yypyqiYKPduödi_^^b_U_snO@EUku}~kM39;GWiuvdHUTYalpȹlHGd^\dx~kE&B}fRMkxkM9Epgký}pdYB8P~lfЩpdWG05O{abangM,Bsa^uȻxy~ZHP~kMTn~ëvv_9)dfasufuеqyRE_nxqdP8Eqgf{{gOHWYTkxq_WkgdxsisZnpfanl{{qkUkifk{g^}xqnbi\u~nHn{l\qu}u}xP@y~viuxsgqqvkuY@HKduǾ}KOk}_\TWguaYUnsOH{gffds{¤vxpfvZ\{ngbPHdqvxvd_xukWp{susdU\_RRqpdKOfÊi{iY9O}u{v}f{pW@@\lynvxupx~n@6RsUugdUWa{vß}vuO~\akg_lDZgg1Ex}KOqxuM@akx\qaa~lPYfU\v}y~}qakMPq{d_Wp}~iYksg\y{}6@s>>bqG_lqunTkp^kayaqqluvf^Tisvdqn~xiskZHk^vx}~vbqlWqq~_~qdqqaGaivn_RY^b=WiUpiR_\MYxyqgxxvuffuJBPng~Z~^8=\{{l~âuqqlkxfqqqlbqgxuu~~Zinfgdlvl{suvvsyP>;bs\ya}ZZbb^qRdyKBv{~}x{GM{kqZuf^TGEkki~xnfsMavU\yZM{palÏ_pdx~qUUdbf}~~y{udMs~dx{}}du}yxsbPfq}}ngxklnRJR{iRk}nBa{vYpWnubk_^ypk{}{i{qdvy{vfYWR~k}U5Znsxp}udapx{~~}qgfyxKTxk~uRanPOguJOdbnx}iWpuqZ_fu^~}i}sgki_pykslxuqpkxaas^\sxud_x~vW~_i{~pgxq\JZf\PqxRbqunWkiyknvsugW_vksn}{pklppa}qWf~ukGYfkdppfUk^\pnxq@;xdYvunnd\pqxsfU{qndssqyvZpvyybkkpkgau{v}xlbMCT_gppq~}\UnfYi{~}bZsnZWxiukdy{~fJasukJZbnd~qYkifi{\K^uxubTk~p\kklPJabaxaf{~~svUv{ZWis{plu~bCJ_nnvflfdv{}gM^}u}}x{~}uyWHE}xd~ZEMg}xk>B}nqupgsMnMRkskn}s_R9=OZ_\usgKJnsanfiJYdgT\Wkv~p^^lu~qkU>BP\gnivvnl^PEYddid_g~vp}x~ZRfvpsu~usvRkTP^isuiv˩yy~qgWEZba_uqfdibTEPguȰ}nqZCBWgvͶnkavYKT^yuȫfPp{kigqlq{iy^OUUfv{sTTdaUdqk^KRTn~î}lsTfxsYp{Y_{^EUWUi{uvg}d^Ydin{n_KP^iRav~udRZibi}sifaUHZnba~kTPnpy~_x\yORviYsx^YfygZf}nx}pgZP_q~nxlda\KHWgxknibfdbuydO~~iZi~nkZs{vqYan{}pdROfkxk~nPZuynl}y}v_aRYlyixq^pyU_gYiy^nqaf}_Y{WYg^\~U^pggaUssYl^Zq{fl}a^p{fx^Zni\y\Raxy_yyPTklnaTp{snZuvaxv_dysykgxy~ub\bsup~{niuylnpiqn}sb_n{qsysunvy}xp{{~~ldiky~y}kfnqqynpu{lbgy{s}kgvxp}}llpqx{lfgq{yuxyx{{qpu{vnv}skuy~vp{~vsqnv~vvssqv~y{unqyx{ss}}plv}pluy~yy}xllv}}xsss{vnqyyuux{yy{ysy}~}}yy~{vsqqsx~xxy~xqqx}xy}uppy~xsv{uv}{y{}y}~~~~{y~~yxy}~}}~~{{~{{~{xy}~~{vvy~}xy{{}~}}yxxy~yvy~}{y{{yy}~~~}{}~~~{yx{~yy{}~}{{{~~{{}~{}~~~~~~~~}}{{~~~~~}}}~~}{}~}{}~~~~}~~~}~~~~~{yy}~~~~}~~~}~~~~~}}}~~~~}}~~}}}~~~~}~~}~~~~~~~~~~~~~~~~~~~~}~~~~}~~~~~~~~~~~~~}}~~~~~~~~~~}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ t l @O         /2$=?,99L6.j2$؞@=y!u>-tjj2$> g2$2$6۟ 3V>_Rˌq 2$jþ6d6o萻ndo2$MԚ/L;2$P85d}*m3 2$ǦNy@&Otq; 2$jfFAWCd5* 2$V,]Fn"[w\j2$G5'2 Z2$9Ugs|g2$~,U5Ad62$'P5M2, 2$ߴսn ^xD 2$0"*M,x82$^>ɇK2sXB%$$2$MG ڢy/z,^2$jK-}SYN.1"$2$>X p=#$$$2$ 1Ma4V'$$$$$$$2$XhȍM,RcCVX(2$xR&VR|+$2$]ղN*-$$2$#1Ĭ U(vW:./$$$$$$$2$hCcpYEAY J 2c $@,g4BdBdd 0Jp p <4BdBdg? 0D <4!d!d@ 0Dg4#d#dd 0pX p~uʚ;2Nʚ;<4dddd= 0:2___PPT9/ 0?- #O < .Regression Models & Loss Reserve Variability"/..Regression Models and Loss Reserve Variability//.Regression Models and Loss Reserve Variability//.Regression Models and Loss Reserve Variability//.Regression Models and Loss Reserve Variability//.Regression Models and Loss Reserve Variability&/ ."Regression Models and Loss Reserve Variability Alternate Loss Development - Method 1:V.&.Regression Models and Loss Reserve Variability Alternate Loss Development - Method 2:W.&;Regression Models and Loss Reserve Variability Variance Estimation-Loss Development:U.%?Regression Models and Loss Reserve Variability Variance Estimation (continued):P. E Regression Models and Loss Reserve Variability Variance Estimation (continued):P. 1 Regression Models and Loss Reserve Variability ,2/0Regression Models and Loss Reserve Variability ,1.Regression Models and Loss Reserve Variability Log Regression Model:F.Regression Models and Loss Reserve Variability Method of Log Regression Model (continued)V\. !/bP ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd @ ? _d@vP U@ d` n?" dd@   @@``PR    @ ` ` p>>A 0 )! (    0m   U!Click to edit Master title style " "  00p   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SdB   <D)XB   0D   0w<Q b* 2 H  0ηo~ ? ̙33 Default Design 0 P8( x    NUgg ]"   v* D""DDgg  Ntfgg  "  x* D""DDggd  c $ ?B 6  4  Nfgg  D  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  Tmgg ]   v* D""DDgg  T<~gg    x* D""DDggH  0qi6Ɍ ? ̙330 `x( 8( x  x NDDgg ]"   v* D""DDgg x NDgg  "  x* D""DDgg x Tgg ]   v* D""DDgg x Tgg    x* D""DDggH x 0qi6Ɍ ? ̙33}   0 ( (  x  c $      0 % ? Prakash Narayan Ph.D., ACAS 2001 Casualty Loss Reserve Seminar2@(2 > H  0ηo~ ? ̙33  vnp(  r  S x     6 - 7 2"  6hPQ kRange for Loss Reserve: 6 2" " "  65  p Ultimate loss will be different from any estimate A measure of variability or range of loss reserve is needed to monitor reserve levels We have methods that can be implemented in EXCEL to estimate reserve variabilityt4XS4  X  S H  0ηo~ ? ̙33(  P(  r  S ̑     6P9 c!Ad Hoc Methods of Reserve Ranges:&" " "   6P* g Use a % of ultimate reserve based on line of business and professional judgment. Use variety of methods and select a range. Use high and low development factors (various alternatives). T,?T  ,  ?   H  0ηo~ ? ̙33b   (   r   S 4      6e ] HStatistical Methods:" "   6 e`p  Development Factor Variability Models (Mack/Murphy) Least Square Method (does not provide parameter uncertainty) Log Regression Method Variety of other methods (not discussed here)'4 '   4    < H   0ηo~ ? ̙33p  (  r  S %e  e   6&e`  J Notation: $ "  \  S A 9?? H  9  6,ep d xi, j = Losses Paid (reported) for the accident year i in development year j. (incremental losses) i,j = 1, . . . n. j yi,j =  xi k k=1 We observe xi, j for i = 1, . . . n; j=1, . . . n + 1  i and we are interested in estimating yi, k and variability of these estimates for k = n + j  i, . . . n.<T ((n J ( ( (   (( $ ' ('  H  0ηo~ ? ̙332   Z( x   S oe  e Z  S  0?? 0   Be/,$ 0 DAssumptions: aj independent of accident year All future development dependent on most current evaluation di, j are error and are independent of accident year and delay Expected value of di, j = o and variance may be a function of yi, j and the development year Note: We assume that losses are fully developed by period n and do not consider tail factors in this study. These assumptions are helpful in deriving variance estimates of ultimate losses. @ vP( @ P(<@ P(?@ P(^@ P(@ vP(g@ P(Q@ P( Y:'8  @`  c $A ??00   B|e0n* j*Regression Frame Work for Loss Development$++H  0ηo~ ? ̙336      0^ (  0 0 c $\e  e Z 0 S  A??Z  A` 0 c $A B??,Tm B"  0 HtFe/0e/`,$ 0 vUnder the assumption2p vP(2 0,  0 HOe/`/0ep,$ 0 (simple average development factors (SAD)()p vP22) 0`  0 c $A2 L??0c 3  L 0 H^e/`/0e ,$ 0 hare best linear unbiased estimates (BLUE) for aj and`5p vP22. 0` 0 c $A* Q?? W  Q 0 He/`/0e ,$ 0 <are unbiased estimates of sj2.tp vP22 0 0 c $A ^?? 8 ^$ 0b 0 He/`/0e,$ 0 Pare unbiased estimates of ultimate factors and ultimate losses respectively. And6Qp vPZ2P 0` 0 c $A f?? " fH 0 0ηo~ ? ̙33     8 (  8 8 c $ a  a Z 8 S  j??Z  j` 8 c $A k?? 6 k" 8 H$qa/0e/0,$ 0 vUnder the assumption2p vP(2 0. 8 Hd~a/`/0e',$ 0 *weighted average development (WAD) factors(+p vP22+ 0` 8 c $A l??{  l 8 Ha/`/0e  ,$ 0 hare best linear unbiased estimates (BLUE) for aj and`5p vP22. 0`  8 c $A$ m?? |i m  8 Ha/`/0e0G,$ 0 Jare unbiased estimates of sj2. Definet&p vP22 0`  8 c $A n??v n`  8 c $A o??vW o` 8 c $A ??  F 8 HUa/`/0eN,$ 0 .are unbiased estimates of ultimate losses, and6/p vPP2.4` 8 HHa/`/0e,$ 0 lthen8p vP22 0H 8 0ηo~ ? ̙33   @9(  @ @ c $a  a ` @ c $A ??.   @ HPa/0e/@r,$ 0 6The assumption of an underlying linear model allows estimation of variance of the estimated ultimate losses. These may be useful in deriving confidence intervals for ultimate losses. Variance of the prediction is2p vPZ2 0LH @ Ha/0e/` ,$ 0 The first term of this equation is parameter risk, the second term is process risk, and expected values of the cross product terms are all zero under our assumptions.2p vPZ2 0+ @ H.a/0e/,$ 0 )Note: We have assumed k = n+1- i and used&*p vPP2* 0` @ c $A ?? ` P ` @ c $A ??l / 2  ` @ c $A% ??{0h H @ 0ηo~ ? ̙33[  0 D(  D D c $0a  a Z D S  ??Z  `  D c $A ??)I    D Ha#pG#pG VParameter Risk 2 DD D Ha#pG#pG {  z(Hence Parameter Risk may be estimated by") 2( DD` D c $A ?? P  D H\a#pG#pG gwhich is estimated by" 2 hh$ D Ha#pG#pG`  xNote: We have used estimates as proposed by Thomas Mack (1994). Daniel Murphy (1994) uses slightly different estimators.y 2y D Hga#pG#pGp[ ^ Process Risk" 2  hh` D c $A ??> ` D c $A 1?? 1H D 0ηo~ ? ̙33  P HB(  H H c $d6a  a Z H S  ??Z  D H H(a#pGpGpG %  zThe Process Risk is assumed independent of accident year. However, the age to ultimate factors are correlated. Therefore, to compute parameter risk for the total ultimate losses one must account for the covariance of the ultimate losses among accident year. The algebra is little messy, after simplification, the covariance estimate for accident years r and s (r 20202x0-2802(0202!0P2 2   "*9""""*"*"*"* ""* "*"*""* "*")"" ""   " "" ""  " 9"*" "*"*" *"* " -" ,) 0 6 TLog Regression Model$H 0 0ηo~ ? ̙33   $>(  $r $ S      $ 6`_  &d The unknown elements of the loss process can be written as _ E Z = B  _ ^ The vector Z can be estimated by B . However our aim is to estimate Xi j and not Z i j . The formulae are a bit complex but unbiased estimate corresponding estimates can all be computed in EXCEL. Details are given in Verrall 1994 CAS Forum.J_>_U/I"  >* """ """"*   H $ 0ηo~ ? ̙33  x((  (r ( S @   ^ ( 60 * Model fitted has too many parameters * Many parameters may not be significant * Tail factor may be needed * Calendar year inflation may be distorting observed observation One can choose alternate models, for example Z i j =  + i + j i = (i - 1)  j =  log (j) Model parameters can be tested for statistical significance. If variance changes by payment year, weighted least square may be used. LUc ""* "* "* ""* "*" H ( 0ηo~ ? ̙33 0 t( $y0 tX t C B 6   e t S e D  e  H t 0qi6Ɍ ? ̙33 0 @(  X  C B 6     S d D    H  0qi6Ɍ ? ̙33 0 (  X  C B 6   e  S Se D  e  H  0qi6Ɍ ? ̙33 0 (  X  C B 6   a  S 4a D  a  H  0qi6Ɍ ? ̙33 0  (  X  C B 6   a  S \a D  a  H  0qi6Ɍ ? ̙33 0 @(  X  C B 6   a  S xa D  a  H  0qi6Ɍ ? ̙33  0 `(  X  C B 6   a  S a D  a  H  0qi6Ɍ ? ̙33 xV=OA}{ DJPHQJ,'U hGBD_`;w݁DCH@ ? ˌo^\DECg=|~}~bot`)4<0dJq#c-W!6Cr?G6Qcϑny֩Ք'OO⾥kTQ) U!s==ֿeʣJ`)n}YyԱKy>h]X?z"!5!q8A]Wf2|/k]j!p={GВazzw_wy38)$\Q )hVT"D[3=tF:[.6Cg3 S cҐ,ra+*sԈUB,:гد*+’+)jG^V{KFVxroFviFvnQkCdÏm֩爅oDL,nEߞn.H xVK/$Qn5F2DHĢV1ʂ -x$nӭJҥ*+{6f?~0[]::_{ystvݟ_? H!S qkq?'bY$g<AZ{ե]s=n*QϘ`/bk"֑PLiBzj끎?E&ڇwR\yMg3(aYy(9,h]X?z-,3k~ F]_fݯ~}5ޖWLi;^A_dh Rm 8{LY\f{ԤRV4+p:Q蜄΁4$NJ~E's|o7]tY+2[-a^Z^FޑV{FVxrU#5i FvnEkOdYÏm*R ߈X~8!WѠ]ko]GHgxVOHTAfꮦfEI*AIPQZx b]uro%A.IGS"Vx,xN݂.$u}L[o(oooo~O=xRr 31ʘvi\L&-lچUtC E:Nm߷_l(> ֶbm~_rYOϙzOvO9 *4/pf-n+d#0@[~ʿ߹!~souzV״zOSC{@ z)7𡗡oAyT5@Ps;z73?63+J{kzbإ=:LcQmұ>L+ulZW!.C(7աNíRJXZT86 KX,iLgxW,tTU|#O\Ժ2 &.'GpKeXשWٗ ƆU1;N%R4!/3Gχ_V_Z h_#W>$,#fEQܵ~oďmN|'?^$'{Smk0{­ou"]&~V\jg\ψb۝xψw-<FowO$Ƃpco>@' ~l! @ݔ;(;ZXOT}sB3C-<= zmVsi }x"h"[/SdU˪&L@}- F+TMv(Co~aEثne6 й&ѥʿ޶O.r^>| 5u3:,D3/9Or5|!}~owȴ%E99)%,s޴u(qxWMLSAZ"m_5Ę ?\(&A#8pKh RQ&Ջу5rI[ u=~0 [1⳹\6h]26C.6)HⓂ0t@ *1cl_t\]wG̠q}!)n3pq8ahHs*Tĕ(OToO4d?M:Jyy͏&le *rkZRA?1ya˯*錝9M##X2nm#Rp#e3ͭu߽ RYW"5d}c>{=o}>3!߸Jx_>f3\V'Н'>܉_Kov1&'z+sxkxY 0^x(*q^םMEȟ^V"خb(Fd0TXh*R =>ֱ3nzx#jpn*7et cC PۘArȧulv*&fz,R,gbXc'b bZivJ|g1If8՝ºHbnKqc}qL:7wU b4g*xW]hU>L6M6V'kj~J1*p#)n&M\)J"}BC_TRD[PWA!{g2wfSZ~{~fGsY5ѽ`j>S,+W7関e&2}󐒭mҿK!88)ldVTڢą|A} g І|:\ݘF0A8ae@ʩPXʿAx jc_Q-Ӟ@{}&9\QwPV@ `+r-mȷ#oCCsC!߅\ܠ6 ïeز>GcNx"rvwRDy}'r['T&u%PcVKhlư ҬaJsiq4 $FH:9SEܝ6@ 7ya{琝6&[҉&Gp㴪q9(&<1i>WXfJh>hj\S+{Ε=RʾNxnYeOv5:0uxI^.Kċ=P6r7 8nx", [Ŀzu8nx",UϞ)`И;?u+Zz6YI Mpi!v#ʓu=Į`&M*|8U/Wr?>< /ZS.6Xϋw62ɭ_Pw?ДV_n$f$}M3 ' ǟ fۛ yJJϗz8ښ2@9@#W"U ʁZO9 znmbeb˖PWTݑ9r($6YJ9Y^yк>l1R}KWj3Ea%[Od-Uz48*3liLKW:?'}ULw$5LتoHݡݩa<-3U~UݑXx>&b8tHOV3ՋkDf# G\|t%v79.TG8;K xkmzp )Yޫq;4g 4){ngʮH} \/ailzPIdQM~>"He0*0:(oK\b7RۋwJ" lf)1&Ҋ #p5jv`FK*s0}Rʞ-D~*V2?xVkQvi|Pqh *C$%)ɦiR5!`? IIo& ƙٗuIE7"J Lvf޽o΂v:քbTaZ-W[TtQPǻWɇ9J@Pc{|!y}z|i[YZHk3"d! 3~=P?` XՆ#O3rrOJ*Ki((_)XZ{]Y@3 هN.eGܢ$aLjLfi=_/xa#UMcbdK|^)#Â;|¥z+C=~% ZFPG)Uz;/u1/1)uo!A^y;(G61>Y}C6IVk8Yo;u~%^d9Z <1a rd:LR;g#QV=rO (U,[F2tјM_1\yeE*\pmwCjJxj癲Md﷑YArWzTO>.2VzvɾIT~P0C'Q'87YW>LC4˚/"ȭ10 ǡ%9hY]vu*'.\ %5r{{9wjM Z5 7#}ܢ&2Os xV;OAy BD(J,D" d))sl>ݝ-PDO4I)$?!M~-fa"2 ?cg5o3?|=XE xL ,w8x{+bG8"g97Fuj}b7ju_i֊g>-]S^bP2ӯtuZ ;G۷? Kq 5+ϡ=h]ʣNJF}=9׶򎜛~i"18qúB%?CHeK{^%sBzu{e)j 4փ\>/x7v1sE&321 h΢ILFs:-if}*" ".-Nd2/@tE~Ue]HM}iX3 ē3ۖbdJBU\"+~lfv@=G,|#bbG2^?yC~HxVkSA}JmZkcY~V(jŋ1$J[Eb  /T/*x ^lgv7Ԛ ݙݷ/_x2w5 fUPncZpgl;(̠54YZۢ~91%NsRGOe9VL.9Sjx6m ȝ)Jⴋ 8o`8臁됟@)?ٟm7l?%\^7󀖧 QQ/j Ox@=wT: |6D]> +*\ >@w`,;4;p,jڷRkʁ|q?x PJC AcX")9J^%Mɗv10dO;gs~|0T-5XĪH3~aC`L_<uiLus"sjFmL@k{68cL7j梼ʟiFq4if/_?OlQ xFՇ‘P<dEQ8>L@f /o'𫕄S!|oy6Pjf3cב_cn\x@㴸&Xm$-$k<).OvIiw^|; &23;Ao-l"ヺ*# דi%F»4.8exܵsPi+W}3D1kA]˓qܛJ$C$`a qA{!.:{ӋjfT_-2?8|xQg D0XQlbՍ@yVf~O^]|bV'~e|ZnXO7x0>w>"KZ=!~IhU0tF;Rg4 xWkSAݗ潴IڤUz *(SIIB#V,=?z"*ċZKBA/?G c7W3=֝r!Nҁ3|* 0? #X Hs4?)8t_GߵT[Mʦ7; 9 xZ&Dm{]gj^' L^ˎgrѾщX.D;6/KiV] ϕC4qO>DKH WSLqaig{3mp+{# fOMYyx} kXX.q.?BWN7.#D6&GݧTwlH߫!x.GO'gXQ8]@>L)[_#BO*vדi%w$į&eS[VQs~+\B7jͅ ggAgw>3J9ǿ囫v7^9^1)^.[oh.[ `>={=e?XBhXMpޥFK{/#~Ro~𮃺]ԘA<qԟӐ)_4UDE=PLDO bg@ 00PKѫyj5|ؕ)C"_ujVy!RmRlfī6JP?(+ ;.g+$AOeKYK))v*AW%LQJ(L Nsx(Rڥʢ=C~öt/12-VBUdžl6(@G\-1%)@XRc–lM@Lί.dMNxW]lTE>ݻ.R@֕B-iI!фb blkۅnVbh4!5iCI}@h *?a93sogVxA=߹g9s~Slx❦{Ul05_qy_hPŇmTTv F8ΏZO3|NڕqsE51 os|Ytt_JO 9pqJ~_yVKRF\ɯ:rXj=EY?j)ܭÞEVj}8'ܟG7. Kla'O|@[;:z:^njKfzj2J7:4gCM%\f~e^_oBWۦ{nT;X%_B9~r>e`+`7\}7#;TIFnBІry棁 '+䙎 N |Ҽ4) _hTS([cdgy2_Cb9^\_"Njgò~|7ij^ۗGfUû rV:g3{= d_hMc[{z; _ PIuIa  {KnE:@" ѥҏ\==x-2^It@ 2pL' ^Pg a;F\p'9It21Xs1v}2Ù MAXL/M{ Rx'$Pߌ+1w{K Qx9eW ,+J5BWf!SxnDt6]ܰK?ٜ~ܡDӏffP_2G/ɬ_/}֝v6d-`R8K5NI7OOMĝ rvt.*yOҩOvi\RV:P}~5hF 1a5(ܐ%LXK^3c4+$cx`Pj COr/d^ ;T(NmXLF~ѕRS 8`gw3 ϊPx۠Ke^|*QL>7'c)s:QGN\nћ4lJZ  \O zqL|7m/uKKILU/zZRo$*؊[`M%Ӊ1lLdӱ m9 WL}4h WO_"T4hLˈ܁A~0EP+v7ԟ GC },tE0 HKLY">{L<KO]=us?HJeaoozߪ+kfi㧸&y)LG'ulv˗: QjfhbNpx_~i~WNeVONaPb9Z~< D_'.@s3pa+ | K wʾ!kZN:b`GORm:nr;r8 sX#IduSrAe:>)'/,loS) $xXiLTW>a1 "@EMY\[*6QC: 0&ؘnIJ.&6i6hGz} ?j|s{{νޛ\=ZP`b25o '&''˓# ڰB=w TD4"Ɛq]O4h.{?`Ƙcz #x[rm˒~'5e| $'Rd0ohsF9EwecO{!y[h6,a{ط?0XD"-6Ii H!LD"!rň%<2D>ƒ(@"ňr[2D9Qi̥ UՈ5jZD {@MoIbSϽгr`[g{?j =}NVQRSicuIJ*c=g~Y>@?W<CV pu0;n L̖bvEq~DZȯɒ#v.Y}n+<{<7󪟇q!B pӥmXdyOn^c2~}mzDŒ~˝6OSɇ$&\T=ڃa/Y GTDh?'>goDf?KX?Tg3'O͝>o@}^vaUI+Ac56fYL߫<)g07SٝG j:W٨}֨tI7vSyc"~OlT=.*C;|$Sx.8(&o7y)? \Sg ZC3%S{ߥVOop^-ʍJr_\;3d[Wof71eƋ,N{kx?tUT.U[V.-˩}R1/nM/,K?ˢHi_]2W>%Oط=;k%QX/ڏ*cz2gub<1QZ2Ǩ2 1Qe_Ϩ2\Bm. }B!ߝGӖP>y2+I߫qTNjrnIȝ ;Qi4T8U))+VPKT~y)Ha5 pR^$ʵ?X&Tϡ|;_JS.\ٙT~,kt<_EiŌWߏ;ُ7~(o\ͨVQ~r}A6I"Uk)(|RʏۚV qvbS锟CY9{eON0ރ]Ho$˹M]|[n6 ؊`M$6$/ր|bDQPKb|*Os+1{"pbN<|Q1 A=ЇĚ:v_ '#J_:?e4g0=|ƃI9-{x,">Q ݹD*,Zܙ= !߼*A9=>a0&#GLF7@H߭礻u}ћc^ >g>g-!xVOAl[`)R?P9x b6iM -tKiԃ!#1I/x04'OGH .MMtkf>f{O}7vЂPot!f(DizpٍC(o0S(SA p轈jk+%#<Q*_iֽpnɗwb"G-Ͱ!Es<~k_AmQ=ckg\tY17ڰϾҟIջ~s/AFnaw޽f~ ?,l{~&rwL%6^ZJWrE'6Rt9TzDbν*v9u0iJ״de5=]Jr3GH@q_q0]5=QbT^c [u[ 1NW%%{]ni?7ԟDd:WȖcٕTvpJyڵ0+=zTu9Wc(Ηz'laWa^Qr1}-'HZE o}f?!<3E'=cL=EKmOՀ; )Sr%[z&#T-Cn`X:[Df` tl-$%S*M5l=:hf͇5hZkN[9ɳЕ(aN݃-4Բ[9F7?6{h<8v xV=OA}{6D)JqE"*Ѐ/; @O4I)+'H_f|ECww>vf>?`)t F v1X2qw aZr x `#>zK?#ouju5V7bkPQLYBz{ _QD`)~}Ey4Ky4e׮smK!ȹ?B?F|@̀xXWg|`(lr{4}%*ok9<$Kiy^/3>hW{dJ)+z +*V􁦶i&6vYEl>v:9|?_!m7Kcm:H$"#CB7C~!Ȟ' L>I?nF !=}2b-rt<~Nf..ȧL59X,`Ѕq@rbOo•o^XM?,kI_vO"*dD ПYdM32!#rO V lD."(@"O"%RDb:U"Ոkk5uZzӈ: m ElAlE+/ /"yig|MU1LV{g@cޞ}}v}A_[g._MKik3FKj\wl_R.` p#a2V-AgI(%h:#Z5. $Nl"u_Mp{g{.dsCd.&䌾,M_?-XD4v #1Clz!R@DK~2}?dӏr_&~Z[Kdgӏ_c}ZgPO.kh}/|kR9u{Մrʧd~"B .va;t :p]s0>Z?!I=IɲW<w?T{ پרVyfzK|'.ϻ9uDikC#N?VʏND[,O[?U}OPJw&;b:fc S)=u}Lu}F[,5.*/I*Wy a3Kq]CWxUɔ9T^{ _+R'C <7|N5]kk@t,Nkʘ"|[hUt4MAi`>$jim~fB#e#' C#Q}JLX?wn8Ї7I'N6PLo?T߭b-nR,U )|[W M<a 4Ⱥb <CXL>7Xs0늌AaB71h"'U=3G=yv7y[dc p <}ì׵dly.vWk4~)LD!&MG7YJTpIc'YYZ`nk\WDD=XcեTBb $BN,sh!$B-j TE !,֓+mr),*)Tc۩L7>#6b|Fc2yZ Q_ A&VNE`wιImZ6d/|ws[ ?k *%]C$s 0)+++z =V\+Lg:-CyA*uiV 1ݧ;] Myw'axS9Uizk/+ #!t0;Tm~?!L?;? SLD~)Ʈ<;:& 9l#끿h" &@݊m;B#DnG~y3ȻzIÓ-Q{O5p$ƩdD>~pt*e{y)(xyyB^S^gD_qrΏ1i+Y_`TM|*Mɗ4\ӥŸi:W5_ #VZEGdw. },Uv?]7?^w\C!|Dd~83a=ηqivsF&5T C> k4}xX:~46݋Ɩ,,535 Q$bΉT]{TCujŴnbpc?`MIt2uN)'7/j */2E"_:$RSv-{ccGzsiꟀyVlJLU_q<={ |_~Yl6ac(*:Y,DyQKo-ckƒ. Ceqqĥn,K][ڒW樣\M+a.yYԍ|;R+F)g승uRX1]h>LCM xV=OA}{M@B)@J4, _`; ||݁&UOCzTO0J6>f|f"2 zؙi )42%l `ɸDZ+!Cr<£OyԨ] ) w<j$%ӶrX:uRtMYʷi"CU\O~_7EyPu Xk l_~ulH;R5:w2iW>ϹI!oɹ?L?B%{< +T37݌T&o޺k*o׫ٹ c4փl_|x??&ngBr̐RʊaEeb@:s _Bg, w:{>Ҍd XѺQ#z2WΗ|C~EW$"c oҲD&ڋg4 ē|0J[1vkBU\"+~l;#_?.p HxWMhTWo3$ɏ R(`"d#5ҖE"ǧ-*]4hnJYEtպԅW颫{{LA_ '|{Ϲ~·h0h4;jS-%pl-zhͭGqÍ9-zt eՐ$J`(x, RcyѶmWܘ2$g3")aC|-(Y|i)g )?d>e>*_tr6cp|l#$Nww^t I .ۢ)ƟK}Åӕr|;ʥ}Nm|0Lܚr={}ep^>bcU\V˕aM/bnQ-jȶi;/Wc4m=TUm~`ɾaj?GG]V_}N]㿚~lDWw;q6ٍh_eLp?S!4SK~}#,c3ma]l7xx򟤏(%3*w pc|*o@x6a pJd<j2l_7Ka:!S䨗N9RF<_e8 o=9pM1];~M̓\Ԗ2m; {̝ fKq3p bHB'?EZsjNуk;=b&WS04N*GZ,k4&{X<"[]`is8O_CA%:8ҫ,Mч(s$^QO4LeKHr~iPA%.J(=te,hK vຈt9np9C͊5M)@#l,I,I`$%$+eKY:W~/x[o xWMlE~3ko8Iӆ4n]S*qLH T USUC]5ۅF\\[,TDBBq8A@U(P8r@U9 z)Ulޛ]v;U[=fޛo~̎ڇ y47;ʘR!!phXōuduZC*qç,0= Q6aXmypQ~IV?rwih LyNBzUN13xZ8 b?Uw#?4V4`xZ>5~*]Wt& چڎځ ]@srN{r`l[PPè[QFP+uYa3~p4SwS~5+#sR\62-RILcǣZ'^g}%~Sf){E-ez@R,b*a% 'JF8SAnŵYߩwBy. +cLoȧ 'QwyeN\/'49ʝ=frW"#ArTi+㙊?r7ÒN\IfYȋr~x*+J+WMg҅D\&3D=Q J(<=N8 G;惄+|՗Apո%ᬍQxZ[=(4Ntd|$\Uބ𨍿eNkojG@˕t%2 L$ ;g}1'lrm<yMpp5HCwd7Ʈ:Jx^ya¿+M4Bx\vwx\9]&L 4Pc o8WbG' t5e@LO;ԡ<J1ꙌWGޱsVRT,x >ȺчX٬ѥzhn!hCThF$ U5$_WfגMe*S|ȕY~yAlbeT H {tFZSʪaxf7aN XigN6-#D+9j_:ܲZZk~+0N ld"K%VL&2D (3Ue &?.(/r߾ź  xUNAvP~% cI0T&Ɛ(&Q^ D O`Xi74Jg`+^(ȝA.s|t_f.oc:4 ?|6S" ðcOCK&?CtQ:T0z^R`쾩^w41EW13{>NAF(u(rr_ԘwDB>U{\gq_[_%&`NU0ko-4j|\x!2mtܚēX;/z+ye"EI}DEX+Xh &΢R™rk],fS$E?|B[NFejPw+cQӖc!cȈjקQGyb2`+^ONyO/WpA~[oԡl}纄Oj!lڀ[N͏Wt~ \W{չ _ɫlz6gE2K\2m[AQwëDۙgoI/ųN^z+cx(i#YGx"YIFx$,y/Kr1a/=:(6G 8 5O;rs,u̹+Ggw%>h>O; '=k̔G9/eX]˃T"k%nZT̆JB-NvА7ԪhۥwL]zKJ9rKhio|&]:c^a}u9"\Mu<RF\"vͪVq6֜_/%l%5\]S 5JT@{I! ,A o$ރ6iꆧ[Bċ͔WF# 7PoheY^>v_~Vx|.!5јrmxVk[U?חMt۳Ү+VڢceA$LY%YL ƕ 6TP?M؏OMZ *,K<^o2 : '~=|/_ތ?h@ρZ;X) Wk'm}Ew-m E_:91,?b<[t\ȯq]7Ϙ)/iHS'8ivv?g 13-:)fjs| !&~S?ЂuZ7}y@g-Q;Cې;;A\@iPM^+G?Τݣ7cL2wĔ% K3>{ON+|#>C>~qާ.]?nW~NFtEG=6;xm2yO3l2uPikcE{%<]zdEc3)EVᕶ}a^yŝK[0Li/|o[[+{$7MxKo+GvNr;_>r|=]jb'n_:AP545q.1{& Tklf4spK;(wQhUbj}|[N=?8SKp`Tw__6h1a5.g,,bG. QE.FzVZZ*d~ټ߽j ,ZJ_(ihi>=~> _hSx oxGKEW]2z<ZKĕ+!]b%)t+jJC"e78HLM6VYt`%Y:48*#ͬZpKxVS(u<7CДxەLɿp_R=z.(|Kl`=Mm}WxApسVx$[S_#ܤ1FRLG]{m<ʜ+KiO]NOSe1 T=PR&n!Yqx hjGlWK ?> ǰi *&Ө| Zd7, b(xEM嵊k: Kx+dz-}"I+Xʠd ް'=׭ 4%0f'|(jb}3``MCtK_* X#HB,0Ѕ/lWhWO 9UD z/ SY cp9@nH5fMpOFwj"Zrܟj;sd8k'\٧jK0|)tzwcR.\ @ cCKQ6C]׉ a] A`VU~+ &d:_cD[҅Q{LWtgXys8V!y")wYto9yDHZ@tBK{d;̛ـz\hәF'%b0Qlݲ\UX< EoGH-V.L^pWC60ho|Z&OO=?vy+,z=ɻ.$5,K}?7'gҎX ۳^-]0=kWu%o26T^sRfRhJbW8qtUŸ\ hK,o I2Cf)K`-uo]7z!7CRac%݃ 0ͪn Y_^OګwU^ r$P,pp"nf':܃: ]H`O2ʪ >f< .P*KL^sL֮wTUߤ/1%誳E|}[FY[{@/ly{%-ݤ$䝤P}Wڤ Y=zKKVl gn7P6ejph xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!58tAFf ہV30d'2b`bDD`;PtGC y'bOzC? rB @6G&`T( Er i= Ē<c=K0\ȇqXn*$&%R3*@!2 8xPaX)uyb+C!C)C"03O02Je`_P٣LB"P f? W xUM/A~f#QP0"S\ \*ā ''∛+@4"[q)}6}?fw}>ܷ=u?P19lL a+bm6h(;G)A nb E՞|icιDmiR6Lbb:g|ܮ?BAXj)@r~V\?E_>-=*OY_\QVQ{xiMmj' *E XW-m[z$Rr "#Dљ Am%k.+s(I91}~*9ne-Y],%i S rq{Zѭ/,'ɷ00.lMsY=̯2V#~Z#SXEyv^\Y1DWX`I1p)ڥ41,Ҷ]zr}n&D%VY xUM/A~f*H(q4NMP"W%JѮ~8 _pq ?@$s $NٝM#g3cfyw}30 U0ҫaf; C{02oT-zVyr ]o#L 9eXk(~pn'(v+l8~ŗ(sr_(g˯GXi <닒ުj6^|A ։?JV~Rբ^3e,Y=/䚜 Vq&. ˸=Z11?DD1$nxL,c8`G8FX$41\zrn&DsUxr$ wg{o7 "q$ PvwPc-0!%:pc(=8/"2"4Vy;B@@BF^`aK>MCPv;Tf X[00_3?~%U^-`3b0-K8dOh+'0D hp    ( 4@H9Regression Models Underlying Development Factor MethodseKaren S. Kaufmann U jponiskeKau66nMicrosoft PowerPointder@,@ 1@I@@|2<6G   0& &&#TNPP2OMi & TNPP &&TNPP    --- !---&fq-- $moom---- $gkkg--&&y|--%zz--&---- JwSwgw - @Times New RomanSwgw( - . 2 1.--r-- @Times New RomanSwgw - .!2 Regression Models  ( . .!2 Regression Models  ( . . 2 ]&". . 2 \&". .+2 tLoss Reserve Variability    . .+2 sLoss Reserve Variability    .--'W--  .2 VPrakash Narayan . .2 UPrakash Narayan . .2  Ph.D., ACAS  . .2  Ph.D., ACAS  . .02 {2001 Casualty Loss Reserve      . .02 z2001 Casualty Loss Reserve      . .2 $Seminar" . .2 #Seminar" .--"Systemwf  -&TNPP &՜.+,D՜.+,D    zCustom RLI Corpn{2 Times New Roman WingdingsSymbolDefault DesignMicrosoft Equation 3.0/Regression Models & Loss Reserve Variability/Regression Models and Loss Reserve Variability/Regression Models and Loss Reserve Variability/Regression Models and Loss Reserve Variability/Regression Models and Loss Reserve Variability/Regression Models and Loss Reserve VariabilityXRegression Models and Loss Reserve Variability Alternate Loss Development - Method 1YRegression Models and Loss Reserve Variability Alternate Loss Development - Method 2WRegression Models and Loss Reserve Variability Variance Estimation-Loss DevelopmentRRegression Models and Loss Reserve Variability Variance Estimation (continued)RRegression Models and Loss Reserve Variability Variance Estimation (continued)2 Regression Models and Loss Reserve Variability 1Regression Models and Loss Reserve Variability HRegression Models and Loss Reserve Variability Log Regression Model^Regression Models and Loss Reserve Variability Method of Log Regression Model (continued)  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles 8@ _PID_HLINKSAx C:\TEMP\Clrs9809_2_appendix.ppt _dejponiskejponiske  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)Pictures3Current UserSummaryInformation(PowerPoint Document(eDocumentSummaryInformation8