Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance

212 Pages·2007·7.749 MB·English

by  Robert L. Brown, Leon R. Gottlieb

Intdruocttioo n
RatemaakinLndog s Rse serving
foPrr opaenrCdta ys uIanlustrya nce
ThiErddi tion
RobLe.rB tr own
Ph.FDS.AF,,C IAAC,A S
LeoRn.G ottlieb
FCAS,MAAA
ACTEPXu bliIcnact.i ons,
WinsCtoendn,e cticut
Copyr<02i 0g0h27t0, 0b 9yA CTEPXu bliIcnact.i ons,
Alrli ghretsse rNvope odrt.oi fto hni s book
mayre pbreo diuancn foeyrmd o bry a nmye ans
withtohpuert iw orriptt eernm iostfsh ieo n
copyorwingehrt.
Requfoerps etrmsi ssshiobouenal ddd rteos:s ed
ACTEPXu blications
P.BOo.9x 74
WinsCtT0e 6d0,9 8
ManufactutredhU eni int ed oSAftm aetreisc a
109 8 746325
Cover bDyCe hisrsitgPinhn eel ps
LibroaryfC ongCraetaslso guibnlgi-Dciaantt-aiP on
BrowRno,bL e.r1,t9 4 7-
Introtdoru actteimoaannlk doi rsnesgs eforrv ing
propaenrcdtya s ualtIyR oibnLes.Brtu r roawnnc,e
LeoRn.G ott-3l-rieded ..
pc.m.
Incliunddeesx .
ISB9N7 8-1-l5l 36-( 6p9b:8ak -l.p6k a .p 1e.Ir n)s urParnocpee,r ty-­
Rates-S-tUan2ti.Iet nses.du rCaasnucael,ty --RaSttea3st.-e -sU.n ited
Insu-rUanniSctteea-dt es-I-G.Ro etsteLlreivoReen.Ib s IT,..i tle.
HG80652.0B0776
368.1'0110973--dc22
2007002022
ISB9N7:8 -1-59968-611-3
l1l
CONTENTS
Acknowledgements
PrefatcFoei rEsdti tivoini
PrefatcoSe e coEnddi tiioxn
PrefatcToeh ird Exd ition
CHAPTEORN E-W hyI nsurance? 1
1.1T hEev oluotfIi nosnu rIa nce
1.2H owI nsurWaonrck3es
1.3I nsuraanUndtc iel 6i ty
1.4W haMta kaeR si sIkn sur1a2b le
1.5W haItn surIaasnn IcdNse o t1 4
1.6R isPke,ra inlHd,a za1r6d
I7. PurcohfIa nsseu rOatnhRceeera: s o1n6s
1.8E xercIi s7e s
CHAPTETRW O- Covera2g3e s
2.1I ntrod2u3c tion
2.2A utomoIbnisluer2 a4n ce
2.I2 L.i abIinlsiutr(yaS neccAet) i2 o6n
2.2M.e2d iBceanle (fiStesc Bt)i2 o7n
2.2U.n3i nsaunrUden dd er-
insuMroetdoC roivsetr 2a7g e
2.2C.o4l lainsdi on
OthTehraC no ll(iSseicoCtn)i 2 o8n
2.3H omeowInnesrusr 3a0n ce
2.4T enaPnatcsk a3g7e
2.5W orkCeormsp ens3a8t ion
2.6F iIrnes ur4a1n ce
2.7M ariInnes ur4a2n ce
2.8L iabIinlsiutry4a 3n ce
2.9L imtioCt osv er4a4g e
2.9D.e1d uct4i4b les
2.9P.o2l Liicmyi 4t6s
2.1C0o nclu4s7i on
2.1E1x erc4i s7e s
lV
CHAPTTEHRR E-ER atemak5i1n g
3.1I ntrod5u1c tion
3.O2b jecotRfia vteesm a5k2i ng
3.l2 E.s seOnbtjieacl5t 2i ves
3. 2.N2o n-EsbsuDeten stiiOrabaljb elce5t 4i ves
3.3F requaenSndec vye 5r5i ty
3.4D afotraR atema5k6i ng
3.4A.c1c iYdeean5rt7
3.4P.o2l Yiecay5r 7
3.4C.a3l end5a8r Year
3.P5 remDiaut5ma9
3. 6T hEex poUsnuir5te9
37. ThEex peEcffteecdPt eirvi6eo0 d
3.8I ngreodfRi aetnetmsa6 k1ing
3.8L.o1s s-DevFealcot6po1mr esn t
3.8T.r2eF nadc t6o4r s
3.8E.x3p en6s9e s
3.8L.o4a dfoirPn rgoa finCtdo ntin7g0e ncies
3.8C.r5e diFbaiclt7io1tr ys
3.8I.n6v esItnmceo7nm3te
3.9R aCthea n7g3e s
3.9O.v1e ArvaelrlRa agCtehe a n7g4e
3.9C.h2a nRgiiCsnlkga ssiDfiicffaetrie8on1nt ials
3.9B.a3l aBnacci8kn7 g
3.9.4 oStfuh mRema aCtrheya n Pgreo ce8d9u re
3. 1E0x erc9i9s es
CHAPTFEORU -RL osRse servi1n1g1
4.1In trod1u1c1t ion
4.2H owO utstCalnadPiiamny gmA ernit1ss1e 2
4.3D efiniotTfie ornm1 s1 4
4.3I.n1d iCvliadFiuimaEl lse t im1a1t4e s
4.3G.r2oI sBsN 1R1 5
4.3P.a3Li odDs esv elo1p1m6e nt
4.3I.n4c uLrorDseesdv elo1p1m6e nt
4.3S.a5l vaanSgdue b rog1a1t6i on
4.3L.o6As dsj usEtxmpeenn1ts1 e7s
4.3F.a7Ts rta Rceks e1r1v7e s
v
4.4P rofessCioonnsaild e1r1a7t ions
4.5C hectkhiDena gt1 a1 9
4.6L osRse serMveitnhgo1 d1s9
4.6.1R eCsaePsrlevu e1ss2 0
4.6T.h2Ee x peLcotsResad t Mieot h1o2d0
4.6T.h3Ce h ain-oLra dder
Loss-DevTerlioaMpnemgtelhne1ot 2d 1
4.6T.h4Be o rnhuetteMre-tFhe1or3dg3 u son
4.6E.s5t iSmpaltiientst o
FrequaenSndec vye 1r3i9t y
4.6S.u6m ma1r4y4
47. DiscoLuonstRsie nsger 1v4e5s
4.8E xerc1i4s9e s
CHAPTEFRI V-EI ntermTeodpiiac1ts5e 9
5.1I ndivRiidRsuakat lPi lnag1n 5s9
5.2I ncreasFeadc tL1oi6rm1si ts
5.2D.a1tC ao nside1r6a2t ions
5.2L.o2sD se velo1p6m3e nt
5.2T.r3e 1nd6 4
5.2R.i4s 1k6 6
5.2E.x5p en1s6e8s
5.2L.o6sD si stri1b6u9t ions
5.3R einsu1r7a0n ce
5.3R.e1s erfovrRi enign su1r7a6n ce
5.4E xerc1i7s7e s
AppenAd ix
183
AnswteorT se xEtx ercises
187
Index
193

vu
ACKNOWLEDGEMENTS
Thee volouftt hitioesnx tbooka s beoetfcg l aannso stwu eisstte htod e ach
ani ntrodpurcotpoerryt y/cascuoaulratstUye n iivnesorufir satnyc e
WateTrlhooero i.g miannaulsw carpsir petp bayrL eidnL dian gaanrdd ,
reevwiebdy segvreoorufasp lts u deontthsie nras ntdrm uocsnttoo trasb,l y
AndrRe.Cw a rtFmCeAlTSlh.,e c iorn tritbotu hptirisoo ajnresgec r te atly
appreciated.
Int hceo uorfsd ee vienltgoh pmea nusicnrttieopx tt fobromom,ka jor
improvweemrseeun gtgseb syat nie ndd ursetvryti eeawcm o mproifs ed
SusMa.Gn ozzFoC,Ao Sf,D elo&i Ttotueci hnHe a rtHfo.rE dl,i zabeth
MitcFhCeAloSlf,E, n gl&i Asmhe rIincsaunCr oarnpcoer DaatvFii.od n ,
MohrmaFnCnA,oS f,T illinghPaesritrnS/Ti ionmw serbasunc rdhy a,i red
byS usaJn.P atscFhCaAkSa,,l sooft hSei msbouffircyeo f
TinlglhiastP/TeorwrAe ivrnas.l uraebvlioeef tw h cer editbhieloirtyy
matewrasisua plp blyDi rTe.hd o mNa.s HeArSzAo.g ,
Thaeu tehsopre caipaplrletych dieea ttearsie lveoidfte hwme a nuscript,
ast ob otcho ntaennpdtr esenctoanttirobinybD, ur tG.ee dr aRl.d
Hartmano,fT eFmCpUAlnSei, v ersity.
Thtee rxetc efiinvaeeldd i taonrpdir aels epnotlaitbsiytho hinsen t gaa tff
ACTEPXu bliciantcilMouandrsii,nJl Bg.ya nl esShainLsdykiniF n,r atini,
anDdi cLko ndFoSnA,.
The aeuxtphroehrsi tsshe asan nkadsp prectioea vteiroyno ne who
cnotritbtouh tceeo dm ploetfth ipiorsno ject.

lX
PREFACTEO F IRSETD ITION
Thper orptey/caarsieusaa lootftny hfae es tgersotw pirnagca trieicanes
thaec tuparroifeaslBs eicoanou.fst eh is groiwsat r ha,p itdhleyr e
growing fodreg moaopnded d agmoagtiecirantil hpa erl o perty/casualty
discfriopmlu inniev eurnsdietryg rsatduudiaenttn heetesas ,r s ltyao gfe s
writaicntgu ariaanlad c etxueaammrpsil,eoi syno e tdh er practice areas
whmoa hya vaeni nteirdneo sistno gmp er opcearstuywa/ol rtky.
Thpiusb lihcaaestv ioolonvuo etfad s eotfc ounrostee Ish atvuhseae td
forn eaard leyc taodt eea acnih n trodcuocuitrnpos rreoy p erty/casualty
insutroapnTichecme sa .t ecraibnaec l o vecrofoemrdt aibnalt yw elve
weetke acsheimnegws itttehir fom rer ewv ainepdr obclleamsT shees .
matearlirsaeolp retshbeean stfoisuc n daotfki noonw lneedegdteeo d
gaianni ntrodaupcptroercoyif ta htbeiu oinl bdlioncgok fts h e
propertayc/tcuadasirusiacaliIltpit ylws ir nietfr.to emtn hp ee rspective
of wohnfoei qrusatl aisafiF eedl olfot whS eo ctiyoe fA ctuaarnide s,
thewne notnt oa chiaenAv ses ociiantt heCesa hsiupAa clttuya rial
Sociaenttdowy o,r ekx tenistnih pvere olypy/e cratspuraalcattryiie cnae
Canada.
Veryl itbtalcek gkrnoouwneld,ee idtgihnme art hemoarit niscusri asn ce,
requfoirar r eeda doift nhtgie swx itot,nh ie m poertaxncte .pS teicot1ni.o3n
onu titlhietyao srsyua mfa emsi liwairctiahtyl caunpldru osb atbhieloiryty,
incltuhdceio nngc oefrp atnsd voamr idaeblnesfusin,tyic otnesx,p ected
vauleasn,vd a riaInnac dedsit.th imeoa nt,h emtaotpoiicfcca rsle dibility,
regreasnsailcoyonsn itsigr,no uwtomhuo sd ealncsdo, m poiunntdme arkees t
braipepf eairtnah ntece exst .
Atlhoutghmhea teprrieasleh netrieespd u rperloyp ertyi/nic tass ualty
origtihaneps p,l iocfta htkein oonw lgeadiginesem d u ch bTrhoea der.
methods hperrheeas vepeno tteedan ptpilailnc oatt ioionnnt lhye
propertpyr/accaatrsiebucaauae,ltl ty is nao c cidesnitc kinannesdsu sr ance,
groluiapfen hde ailntshu arnamdna cnoeyt, hr eerla arteeads .
x
Studoefnt thisin st rodmuacttesorhrioyaun lol ptdr estuohm aev ae
workkinnogw lientd hgpeer opertyp/rcaacsaturiaehclaoety,w eTvoe r.
achitehvatethi ,en terreesaitdaseed drv ised antdop uernscuoeu raged
thber oabdaesorefm atearviaailtl harboltuehag edh v asnycleldoa fb us
thCea suAaclttuySa orciiaelty .
Thpiusb liicmsae taitnoowtn h ettha ep pefotrmi otreTe ot. h eaxtt Ie nt,
invyiottuepo a rtaanekdne j oy!
WaterOlnotoa,r io RobLe.Br rto wn
Marc1h9,9 3