UNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Katarína Sakálová

Transcription

1 The process of uderwriig UNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Kaaría Sakálová Uderwriig is he process by which a life isurace compay decides which people o accep for isurace ad o wha erms Life isurace compay isures hree ypes of risks: ivesme, moraliy ad morbidiy risk ad wa o place a price o each risk i isures I praes isurer charges he same risk premium for group of idividuals The he mai idea is ha he risk premium covers he average risk i his group Bu if he premium is o adeuae o he average risk i his group, he he compay will probably make a loss To preve his life isurer separaes he homogeous idividuals who wa isurace io homogeous groups wih respec o he mai facors ha affecs he moraliy ad morbidiy risk This separaio io homogeous groups is he selecio process The iroducio of selecio does o lead o a improveme of overall moraliy eperiece, bu he eperiece will be beer for he selec group (for smaller premiums) ad correspodigly worse for he o-selec group (for greaer premiums) Isurers eercise selecio bu poeial policyholders ry o eercise ai-selecio Ai-selecio is a aemp of policyholder o ake ou a corac o erms ha are beer ha he or she should ge The process of uderwriig has hree sages: The firs sage is he class selecio Compay decides o whom ad how i wills sales is producs 2 The secod sage begis whe he isurer receives a proposal form O his iformaio is based he compay s decisio bewee hese possibiliies: - accep he proposal o he sadards premium of isurer, - accep he proposal o special erms, - pospoe furher cosideraio of he proposal, - rejec he proposal 3 Whe uderwrier acceps he proposal o special erms he cosiders he aure of he risk ad raslaes his io he special erms Uderwriig covers he selecio process, he deermiaio of he erms o offer o lives who are o i he selec group ad reduces effecs o a isurers eperiece ha arise from he ai-selecio 2 Sources of iformaio Proposal form Every poeial policyower eed o complee a proposal form I will coai wo group of iformaio: Firs - deails relaig o he corac ha a applica was o buy ad he ame, address, age ad he se of he applica Secod deails of he applica s medical ad fiacial hisory (marial saus, heigh, ad weigh, smokig ad drikig habis, )

2 Persoal medical repor Whe he applica has a persoal medical aeda, he uderwrier may obai a repor o he applica s medical hisory Specific codiio uesioaire, Medical eamiaio, Specialis medical repor Isurer eeds hese four sources of iformaio if i suggess oher medical evidece or if he cover is very high Fiacial uesioaire Isurer eeds his source of iformaio if he cover is very high 3 Era risks A era risk arises where a proposal for life isurace is o accepable a sadard raes The amou of era risk he represes he uderwrier s assessme of how much worse he applica is i moraliy or morbidiy erms ha a sadard risk A life isurer has o achieve a balace bewee havig compeiive premium raes ad havig a geerous uderwriig policy I is foud i pracice ha mos isurer follow geerally similar uderwriig policies ad accep a ormal raes bewee 90 % ad 95 % of he proposals made o hem Era risks fall io he followig four caegories: a) Healh risks: These cosiue he majoriy of era risks ecouered ad cover all era risks ha arise for a medical reaso of ay kid b) Occupaioal risks: Cerai jobs give rise o a icreased risk of deah, ijury or illess c) Recreaioal risks: This caegory coais for eample aciviies as hazardous spors (privae flyig, moor racig, hag-glidig) d) Foreig residece: Compaies usually use he oio foreig o mea ouside Europe, Norh America ad Ausralia ad residece oher ha for holiday Every era risk may be characerised by is iesiy ad is icidece The iesiy for moraliy risks may be epressed i hree basic ways: perceage of ormal moraliy This is he mos commo mehod employed I pracice he perceage applies o µ The miimum level of era risk would be + 25 % or addiio o he age I he pas, bu less commoly ow, he degree of era risk was specified as a fied addiio of for eample five years o he age of he life o be assured So if he applica aged is subjec o a era risk is for compay euivale ha applica is a sadard life aged ( + 5) addiio o he rae of moraliy The iesiy of he era risk may be described as a fied addiio o he ormal raes of moraliy For eample if µ is he force of moraliy from he sadard able he era risk has a force of moraliy a age of µ c Afer his isurer ca cover uaified era risk io he special erms The special erms will ake oe of he wo basic forms era premium ad deb

3 4 Era premiums A era premium is a addiioal premium ha he life isurace compay charges o he op of is sadard premium where a applica is subjec o a era risk Deermiaio of era premium depeds o how he compay has epressed he era risk If he compay uses perceage of ormal moraliy e = + 00 where e is perceage of he sadard moraliy (which epresses addiioal moraliy), he era premium is e % of sadard premium This is appropriae for eample for erm assurace For some ypes of corac (edowme ad whole life assuraces) is beer o calculae a special premium based o The he era premium is he special premium less he sadard premium If he compay has epressed he era risk as a icrease of m years i age, he he era premium will be he sadard premium for age ( + m) less he sadard premium for age, where is he age of he applica This mehod is easier o apply as he previous mehod Whe we are modellig era risk wih a cosa addiio o he force of moraliy so ha he force of moraliy is µ = µ + c A his case we ca model he era moraliy by icreasig he rae of ieres We kow ha Where ieres rae = δ δ i e ( ν = e ) ad δ is iesiy of ieres The ad p where δ = l( + i) From his we have c δ v = p e e, ( c+ δ ) v = p e = p ( v p ) ń ( c+δ ) where ( v ) = e The icreased he rae of ieres which allow us o model era risk wih he use of sadard moraliy ables we fid from he followig epressio Afer some rearragemes we obai ad for i : p µ + cd µ d 0 0 c c = e = e e = pe e 0 p = e µ d ( c+ δ ) = + i = ( + i ) ( c + δ ) = l( + i ) +δ c i = e,

4 5 Deb The mai aleraive mehod of allowig for era moraliy is o reduce he sum payable o deah leavig he premiums uchaged ad is called he deb So a deb or lie is a deducio from he beefi payable uder a corac (usually oly o deah) where a sadard premium is payable The mehod ca operae i oe of wo ways: by a level deb hroughou he period of he assurace, or for a limied period, by a deb which commeces a a higher level bu dimiishes wih duraio eiher over he whole erm of he assurace or over a shorer period ad ulimaely becomes zero From his defiiio is clear ha a deb is usuiable i he case of emporary assurace cover I pracice i is used for edowme assurace The mai argume for a office o prefer a deb raher ha a era premium is ha i does o ivolve he policyholder i ay addiioal paymes ad if a policyholder survives o such ime as he deb for eample becomes zero ohig will have bee los We ry o derive he epressio for deb Z () (for he ui of a claim) a ime i he case of decreasig deb We use he firs mehod of uaificaio of era risk Le V be he reserve a he begiig of year + ad V + he reserve a he ed of year + If P is a premium a he begiig of year +, S is he sum assured ad + respecively p + is he probabiliy ha he perso aged ( + ) does o survive respecively survive age + +, he we have a followig epressio ad afer some rearragemes we have ( V )( ) ( ) + P + i = S V+ + V + [ V ( i V ] ( + i) = ( S V P ) Similar epressio we have for a perso wih higher moraliy + [ V ( + i V ] ( + i) = S V + ( + + ) P Because p + =, for heoreical era premium P - P, which mus pay he policyholder a he begiig of he year ( +), we have: ( P P)( + i) = ( )( S V+ + [ p ( V V ) ( + i)( V V )] = Bu if he compay was o solve his siuaio usig a deb he Z( ) = ( )( S V+ + [ p ( V V ) ( + i)( V V )] + If reserves for boh coracs wih he higher ad he lower moraliy are he same, he from he precedig euaio we obai Z ) = ( )( S V ) ( + If + V is he reserve per ui of sum assured ad S is he ui sum assured he Z() is he deb for ui sum assured

5 Z ( ) = ( V+ ) Ecep for log erm edowmes ad whole life coracs, he above formula will produce dimiishig debs, sice he sum a risk will usually decrease faser ha ay icrease i he facor Where he era moraliy is assessed as a cosa perceage icrease of hge ormal e raes of moraliy, he above euaio ca be simplified Suppose = +, where e is 00 he perceage of era moraliy, he he deb per ui sum assured is e L = ( V +) 00 + e For edowme assuraces i ca be assumed ha he sum a risk reduces i a sraigh lie from uiy a ery o zero a mauriy Ad so he deb is reducig liearly over he period of assurace 6 Oher mehods for dealig wih era risks Eclusio clauses The aim of he eclusio clause is o eclude from payme of beefi deahs which arise from or oher of a umber of causes which will be specified i he clause To be effecive Refereces Hylads, J F, Gray, L J: Produc pricig i Life Isurace Lodo: The Isiue ad Faculy of Acuaries Krčová, I: Kvaifikácia era rizika Zborík absrakov zo semiáru Akuárske vedy v podmiekach poisého rhu SR Vir Life isurace Modul F Sudy maerial Oford: Isiue of Acuaries Neil, A: Life Coigecies Oford: The Isiue of Acuaries ad Faculy of Acuaries Sakálová, K: Oceňovaie produkov v živoom poiseí Braislava: Vydavaeľsvo EKONÓM 200