[PDF] [PDF] LTAM-21-18 Supplementary Note on Long Term - Purdue Math

[PDF] July 2020 SOA Exam LTAM Percentage Results - SOAorg

The pass mark, number of candidates writing, the effective number writing (those who achieved at least 50 of the passing score), the number passing, the 

[PDF] Spring 2020 LTAM – Long-Term Actuarial Mathematics - SOAorg

24 avr 2020 · are fully graded, passing will depend only on the total score 2 Recommended material to master the Learning Objectives/Outcomes includes 

[PDF] ARC Conferencekey

of Passing the Exam? Does Percentage Pass 2013 Survey Results Earned Level Number of Practice Exams Pass Rate 5 5 62 1 6 5 64 7 5 110

[PDF] LTAM - The Actuarial Bookstore

A well prepared candidate should be able to score at least half of the points for WA 3 and WA Once again, there's no shortcut to passing the next LTAM exam

[PDF] LTAM-21-18 Supplementary Note on Long Term - Purdue Math

LTAM-21-18 employees cannot opt out) may be lower than the equivalent rates for must obtain approval from the regulating body for such rate increases

[PDF] PERSEVERE WITH PASSION - The Actuary Magazine

success for the ACA from a number of different perspec- tives equity risk, interest rate risk, time value of money and Actuarial Mathematics (LTAM) exam

[PDF] Actuarial Mathematics at Kent State University - Department of

27 août 2019 · Number of jobs in this field is increasing at a rate of 18 (much faster than Exam LTAM–Long-Term Actuarial Mathematics: MATH 40055-6 Students grossly underestimate time and effort needed to pass ▷ Approx 100 

[PDF] ASM Study Manual for SOA MLC, 15th Edition - Fourth - Actex

63 Interest Rate Risk: Diversifiable and Non-Diversifiable Risk 1269 of the exams they take and the not-so-bright ones pass 40 of the exams they take

[PDF] lu decomposition ill conditioned

[PDF] lu decomposition python

[PDF] lu decomposition with partial pivoting

[PDF] lua 5.1 reference manual pdf

[PDF] lua for beginners pdf

[PDF] lua language book pdf

[PDF] lua language reference manual pdf

[PDF] lua language reference pdf

[PDF] lua standalone interpreter

[PDF] lualatex font

[PDF] lualatex fontspec example

[PDF] lualatex fontspec font not found

[PDF] lufthansa airlines strike

[PDF] lufthansa flight schedule pdf

[PDF] lufthansa flight status frankfurt to delhi

LONG TERM ACTUARIAL MATHEMATICS SUPPLEMENTARY NOTE

LTAM-21-18 Printed in U.S.A.

Long TermActuarialMathematics

SupplementaryNote

Revised March2018

Mary RHardy

University ofWaterlo o

c

2017 MaryR Hardy

1

Contents

1 Longterm cov eragesinhealthinsurance5

1.1 Disabilityincomeinsurance (DII) .. .... .. .. .. .. .. .. .. .. .. .. .5

1.2 LongT ermCareInsurance(L TC). .. .... .. .. .. .. .. .. .. .. .. .. 7

1.3 CriticalIlln ess(CII)Insurance. .... .. .. .. .. .. .. .. .. .. .. .. .10

1.4 Chronici llnessinsurance.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10

1.5 Hospitalin demnityinsurance(HII)... .. .... .. .. .. .. .. .. .. .. .10

1.6 ContinuingCareRetirementComm unities(CCR Cs)... .... .... .. .. .11

2 Multiplestate models forlongtermhealth anddisabilit yinsurance 13

2.1 DisabilityIncomeInsurance .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 13

2.2 LongT ermCare.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16

2.3 CriticalIlln essInsurance... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .19

2.4 ContinuingCareRetirementComm unities(CCR C)... .... .... .. .. .. 23

3 Recursionsfor policy valueswithm ultiplestates29

3.1 Reviewof policy valuerecursionsfor traditionallifeinsurance. .. .. .. .. .. 29

3.2 Recursionfor DII withdiscretetimeand benets .. .. .. .... .. .. .. .. 29

3.3 Generalrecursion forh-yearlycash

ows .... .. .. .. .. .. .. .. .. .. .33

3.4 Approximatingcontin uouspaymentsin discreterecursions...... .. .. .. .36

4 Mortalityimprov ementmodelling37

4.1 Introduction... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 37

4.2 MortalityImprov ementScales..... .. .. .. .. .. .. .. .. .. .. .. .. 41

4.3 Stochasticmortalitymo dels... .... .. .. .. .. .. .. .. .. .. .. .. 48

4.4 TheLee CarterMo del. .... .. .. .. .. .. .. .. .. .. .. .. .. .. .. 49

4.5 TheCairns-Blak e-DowdModels.. .... .. .. .. .. .. .. .. .. .. .. .. 55

4.6 Actuarialap plicationsofstoc hasticmortalit ymodels... .... .... .. .. .58

4.7 Noteson stoc hasticmortalitymodels. .... .... .. .. .. .. .. .. .. .. 59

4.8 Referencesand furtherreading .. .. .. .. .. .. .. .. .. .. .. .. .. .. 61

2

5 StructuredSettlemen ts62

5.1 Introductionandbackground .. .... .. .. .. .. .. .. .. .. .. .. .. .62

5.2 Noteson structuredsettlemen ts. .... .. .. .. .. .. .. .. .. .. .. .. .64

5.3 Reviewablesettlementsun derwork erscomp.... ...... .. .. .. .. .. .65

5.4 Referencesand furtherreading .. .. .. .. .. .. .. .. .. .. .. .. .. .. 68

6 RetireeHealth Benets69

6.1 Introduction... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 69

6.2 Valuingretireehealth be ne ts.......... .. .. .. .. .. .. .. .. .. .69

6.3 Fundingretireehealth benets .. .... .. .. .. .. .. .. .. .. .. .. .. 74

6.4 Referencesand furtherreading .. .. .. .. .. .. .. .. .. .. .. .. .. .. 78

3

Preface

Introduction

This notei sprovidedas anaccompanimentto thesecond editionof ActuarialMathematics for Life ContingentRisks(AMLCR), byDickson, HardyandWaters (2013,Cam bridgeUniv ersity

Press).

AMLCR includesalmost allof thematerial requiredto meetthe learningob jectives develop ed bythe SOA fortheLongT ermActuarial Mathematicsexam which willbeoered fromF all

2018. Inthis notew eaim toprovide additionalmaterial requiredto meetsomeofthenew er

learning objectives.Thisnoteis designedto be readin conjunctionwith AMLCR,and we reference sectionand equationn umb ersfromthattext.We expect thatthis materialwillbe integratedwith thetext formallyin athird edition. The SUSMand SSSMused inthis noterefer tothe standardu ltimateand selectmo delsdened and usedin AMLCR.

Acknowledgements

I wouldlike tothankDavid Dicks onand HowardW aters,myAMLCRco-authors,for innumer- able hoursof lively discussionaboutactuarial mathematics. Professor JohnnySiu-HangLi isa leadingexp erton mortality modelling, andhegenerously providedsome background materialsforSection4 ofthe note. Je Beckley,KenBonv alletand SteveWhiteoeredvaluable information,in particularwith respectto detailsof USpractice andterminology .Jessica OuDang hasp rovidedinv aluableand careful researchandeditorial assistance. None ofthese brilliant andcarefulpeople bears any responsibility foranyerrors oromissionsin this work.

Edits andCorrections

Some typosandminoredits ha ve been incorporatedinthisversion.

1. InSection 2.1,w eha vecorrecteda typoinequations(8) and(9), replacing` nk12

' inth e subscripts with` nk+112

The numericalcalculationsarecorrect.

2. InExample 2.6the tablev aluesf orA(12)03

xhavebeen changed ,withconsequentchanges in thesolution s.

3. InExample 3.1w eha veaddeda sentenceclarifyingthatthe CIdiagnosis lumpsum is

not paidif thelife isd iagnosedand dieswithin asinglemonth. We ha ve alsomade smal l corrections tothe A(12)xfunctions andconse quentlytothesolutions.

4. InExample 4.7w eha vecorre ctedthespecicationofK(2)

2017= 0:01 inthe rstline. The

calculations arecorrect. 4

1 Longterm cov eragesinhealthinsurance

1.1 Disabilityincomeinsurance (DII)

Disabilityincome ins urance,alsoknownasincomeprotection insurance,is designedtoreplace income forindividuals whocannot work, orcannot worktofull capacity dueto sicknessor disability.Typically ,levelpremiumsarep ayableat regularin tervals throughthetermofthe policy,butare suspended duringp eriodsofdisabil ity .Benetsarepaidat regularin tervals during periodsofdisability .The benetsareusuallyrelatedto thep olicyholder'ssalary,but to encouragethe policyholder toreturntow orkas soon asp ossible,thepaymen tsare generally cappedat 50-70%of thesalary thatis bein greplaced. Thep olicycould continueuntilthe insured personreaches retirementage. Common featuresor optionsof dis abilit yincomeinsuranceincludethefollowing. Thewaitingp eriodorelimination periodis thetime bet weenthebeginningofa periodofdisabilit yand thebeginningof theb enetpa yments.Policyholders selecta waitingp eriodfromalistoered by theinsurer, witht ypicalp eriodsbeing 30,60, 180or

365 days.

The paymentofbenets basedon total disabilityrequires thep olicyholdertobe unable to workattheir usualjob, andto be notw orkingat adieren tjob.Medicalevidence of the disabilityisalso requiredat interv als. If thep olicyholdercandosomework,but notat thefu llearning capacityestablished beforethe perio dofsickness,theyma yb eeligiblefora low erbenet basedonpartial disability

The amountofdisabilit yb enetspayable maybe reducedifthepolicyholderreceiv esdisabilityrelated incomefrom othersources, forexample fromw orkers compensation orfrom ago vernmentbenetprogram.

The benetpaymen ttermisselectedby thep olicyholderfrom alist ofoptions.T ypical terms aret woyears,ve years,orup toage65. Oncethedisability benet comes into payment,itwill contin ueto theearlieroftherecov eryof thep olicyholderto fullhealth, or the endof theselected benet term,or thedeathofthe policyholder. Ifth ep olicyholder movesfromfull disability topartial disabilit y, thenthe benetpaymentsmaybedecreased, but thetotalterm ofb enetpa yment (coveringthe fullandpartialbenet periods)could bexed. Forshorter be netterms,thepolicycoverseac hseparate perio dofsickness, soevenifthe full benetter mof,say,t wo yearshasexpired,ifthe policyholderlaterbecomes disabled again, providedsucient timehaselapsedb etw eenp eriods ofsickness,thebenetswould bepa yableagainforanotherp eriod oft wo years. 5 Where twoperiods ofdisabilityoccur withonly ashortinterval between them,they may betreated asa singlep eriod ofsic knessfordeterminingthebenet paymen tterm.The o perioddetermines therequired interv alfortwop eriods ofdisabilitytobe considered separately ratherthan together.It isset by theinsurer. Forexample, suppose apolicyholderpurc hasesDI Iwithat woyear benetterm,mon thly benetpa yments,andatw o-month eliminationp eriod.Theinsurersetstheo perio dat six months.Thep olicyholderb ecomessic kon1J anuary2017,andremainssickun til 30 June 2017.She returnsto work butsuers arecurrenceofth es ic knesson 1Septem ber 2017.
The rstb enetpayment wouldbemadeat theend oftheelimination perio d,on 1Marc h

2017, andw ouldcontinue throughto30June. Sincethe recurrenceo ccurswithin the

6-montho perio d,thesecondperiod ofsic knessw ouldbetreatedas acon tinuationof

the rst.That meansthat thep olicyholderw ouldnot haveto waitanothert wo months to receivethenext paymen t,and italsomeansthaton1 Septemb er,four months ofthe

24-monthb enettermwould hav eexpired,andthe benetswouldcontin uefor another

20 months,oruntil earlie rrecovery .

`Own job' or` anyjob ': thedenition oftotal dis abilit ymaybebasedonthepolicy- holder's inabilitytop erformtheir ownjob,or ontheir abilitytop erforman yjob thatis reasonable giventhep olicyholder'squalications andexperi en ce. Clearlythelatterisa more comprehensivedenition,and ap olicythat pays benetsonlyif thep olicyholderis unable top erformanyjob shouldbeconsiderably cheap erthan onethatpay sout when the policyholderisunab leto doher/hisown job.

DIIin surancemaybepurc hasedasagroup insurancebyan employer,to oset thecosts of payinglongterm disability benets totheemploy ees.Groupinsurancerates (assumingemployeescannotopt out)ma yb elo werthan theequivalent ratesforindividuals,becausethe groupp oliciescarry lessriskfromadversese lection.There arealso economiesof scale,

and lessrisk ofnon-pa yment ofpremiumsfromgrouppolicies. Long termdisabilit ybenetsma ybeincreased inlinewithin ation. Policiesoften includeadd itionalb enetssuc has`return tow orkassistance' which osets costsasso ciatedwithreturning tow orkafterap eriod ofdisability;for example,the policyholderma yneedsomere-training, orit may be appropriatefor thep olicyholderto phase theirreturn tow orkb yworkingpart-time initially.Itis intheinsurer'sin tereststo ensure thereturn tow orkis assmooth andas successfulas possibleforthepolicyholder. 6

1.2 LongT ermCareInsurance(L TC)

1.2.1 LTCinthe USAa ndCanada

In at ypicalLTCcon tract,premiumsarepaid regularlywhilethep olicyholderis well. When the policyholderrequirescare, basedon theb enettriggers denedin thep olicy,thereis a waitingp eriod, similarto theelimination perio dfor DII;90daysis typical. Afterthis,the policywill pay bene tsaslongastheneedforcarecontin ues,or untiltheend ofthe selected benetpa ymentperiod. Common featuresoroptionsasso ciatedwit hL TCinsuranceinthe USAandCanadainclude the following.

The triggerfor thepa yment ofbenetsisusuallydescrib edin termsoftheActivities ofDaily Living,or ADLs.There aresix ADLsin commonuse;

{Bathing {Dressing {Eating (doesnotinclud eco oking). {Toileting(abilit ytousethe toiletand managep ersonalh ygie ne ). {Continence(ab ilitytocontrolbladder andb owelfunctions) {Transferring(gettingin andout ofa bed orc hair). If thepolicyholder requiresassistancetop erformt wo ormore oftheADLs,based on certication byamedical practitioner,then theL TCb enetis triggered,and thewaiting period,ifan y, commences. There isoften analternativ etrigger basedonsevere cognitive impairment ofthe policy- holder. Although themost commonp olic ydesignusestwoADLsfor theb enettrigger, some policiesuse three.

Atissue, thep olicyholderm ayselect adenitetermbenetp eriod(typical optionsare between2years and5 years),orma yselect anindenite period,under which bene t paymentscontin ueaslongasthetrigger conditionsapply .

The benetpaymen tsmaybebase donareim bursementapproac h,underwhich theb en-ets arepaid directlyto thecaregiving organisation,and cov erth ec ostof providingappropriate care,up toa dailyor monthly limit.

Alternatively,theb enetma ybebased onaxedann uitypay ableduring theb enet period.Thep olicyholderma yhave the exibilityto applythebenettowhatev erf orm 7 of careis mostsuitable, butthere isno guarantee thatthe annuit yw ouldbesucien tfor the levelofcare required. The insurerma yoertheoption toha ve thepa yments, orpaymentlimits,increase with in ation.

The reimbursementtype ofbene tma ycoverdierentformsofcare,includingin-homecare, deliveredby visitingorlive-in support work ers,orresidential carecosts,underwhic hthe policyholderwould moveto asuitableresiden tiallong termcare facility .

Similarly toDI I,ano-perio d,t ypically6months,is usedtodeterminewhether tw osuccessivep eriodsofcarearetreatedseparatelyor asa singlecon tinuous perio d.

Hybrid LTCandlife insuranceplans areb ecomingp opular.There aredieren tways tocombineth ebenets.Under the`returnofpremium' approach, ifthe benets paidunder the LTCinsuranceare lessthan thetotal ofthe premiumspaid, thebalance may be returned aspart ofthe deathb enetund er thelifeinsurancep olicy.Alternatively ,the `accelerated benet'approach usesthesum insuredundertheli feinsurance policy topa y

LTCb enets.Ifthep olicyholderdies before thefullsuminsured hasb eenpaidinL TC benets,the balanceis paidas adeath benet. Thep olicyholderma yadd anextension of benetsoption tothe hybrid insurance,whichw ouldpro videfortheL TCbenetsto continuefora pre-determinedp eriod afterthe originalsuminsured isexhausted. Typ ically, extension periodsoeredare inthe rangeoftw oto ve years.

In theUSA someL TCp oliciesaretax-qualifying,whic hmeansthatp olicyholdersma ydeduct ap ortionofthepremiums paid fromtaxable incomewhen lingtheirtax returns.These policieshav eatriggerbasedoninabilit yto perform tw oADLs, orbasedonse vere

cognitiveimpairmen t,providedth edisabilityis expectedtolast foratleasta 90-day period. Premiums aredesigned tob elev elthroughoutthe policyterm,but insurersmay retain the righttoincrease premiumsfor allp olicyholdersif theexp erienceis sucien tlyadv erse. Generally,insurers must obtainapproval fromthe regulatingbodyforsuc hrate increases. In thiscircums tance,policyholdersmayb egiventhe optiontomaintain thesamepremi- ums fora low erbenetlev el.Anotherfeaturethat maybeinvoked by regulation isthe Conditional BenetUp onLapse, underwhic hpolicyholderswho lapsetheirp oliciesma y use thenet ofall premiumspaid lessan ypaid claimsas asingle premiumtopurchase a new, paid-upL TCpolicy.

1.2.2 LTCin othercountries

In thissection we brie

ydescribeho wL TCinsurancediersin somecountriesaround theworld. 8

LTCin France

LTCinsur anceispopular inF rance;in2010th emark etpenetration(meaning theprop ortion of eligibleadults withco verage) washigherthanany othercountry. France provides asocial securityt ypebenetforL TCcoststhatis income-tested(those withhighre tire ment income receivele ssbenetthat thosewithlow erincome), andthat isdesigned tocovera signicant proportionof thecost ofb asic nu rsingorresidentialcare.L TCinsuranceallowspolicyholders to supplementthego vernmen tbenet. Policiesin France aremuch simplerand muchcheaper than inthe USA.Premiumsin2010 averagedaround$450 per year, comparedwith over$2,200 intheUSA

1. Benetsarepaidasa

xed orin ation indexedann uit y.Policiesareoftenpurchasedthroughgroup plansfacilitatedby employers,reducingthe expenses. Thep olicyholdermayc hoos eapolicy basedon`mildor severe dependency'or onebased on`sev eredep en dency'only. Theseveredependencypolicyis more popularthan themild dependency typ e.Severedep endencyisdenedasbedorchair bound, requiringassistance severaltimesa dayorcognitiveimpairment requiringc onstantmonitoring. Mild dependencyrefersto cases whereth eindividualneedshelp witheating, bathingand/or some mobility,butisnot bed orc hairb ound.PremiumsinF ranceare lowerthan theUSpartly becauset heaverage benet(around$25per dayin2010) isconsiderably less thantheav erage payoutfroma USp olicy, wheret ypicaldailymaximumreimbursemen tlimits rangefrom$100 to $200.Other relevan tfactorsincludethesimpler contract terms,and thefactthatindiv iduals in Francetendto purchase theirp oliciesatyounger agesthan intheUSA.

LTCin Germany

In GermanybasicL TCcosts arecov eredunder thego vernmentprovidedso cialhealth insurance . Individuals cantop upthe gov ernment benetwithprivateLTCinsurance, orcanoptout of the stateb enet(andthereby optout ofthetaxsupp ortingthe benet) anduse LTC insurance instead. Theb enetsarexedannuities.

LTCin Japan

LTCinsurance ispro videdin Japanonastand-alone basisor asa ride ron awhole lifeinsurance policy.Theb enetis payableas alump sumorannuity, triggeredwhen thep olicyholder reachesa specied levelofdep endency.Therema yb eadditionalbene ts payablewhen thelevel of dependencystepsup.

LTCin theUnited Kingdom

In theUK regularpremium LTC policies arenolongeroered, astheyne ver reached the necessary levelofp opularity forthebusinesstobe sustained. In theirplace isa dierent kind ofpre-funding,calledan immediate needsann uity. This is asingl epremiumimmediateann uity thatis purchasedasthe individualis about tomove permanentlyinto longtermcare,p ossiblyfunded fromthe proceeds ofthesaleof aprop erty . The benetispaid asa regularxed annuit y, butis paiddirectly tothecarehome,savingthe policyholderfrom having topayincome taxon theproceeds.Because theliv esare assumedto 1 9 besomew hatimpaired,andtheinsurer's exposure toadv erseselection withresp ecttolongevity is reduced,the benet amountper unitofsinglep remiumma yb esomewhat greaterthan a regular singlepr emiumlifeannuity .

1.3 CriticalIllness (CII) Insurance

Critical illnessinsurance pays alumpsumb eneton diagnosisof oneof alistofsp ecieddiseases and conditions.Dieren tpoliciesand insurersmayco ver slightly dierentillnesses,but virtually all includeheartattac k,strok e,majororgan failure,andmostforms ofcancer.Policies may be whole lifeorfor adenite term.Unlik eDI Ior LTC insurance,oncetheclaim arises,thebenet is paidand thep olicyexpires. Asecondcriticalillness diagnosisw ould notb eco vered. Some policiesoer apartial returnof pre mium ifthe policyexpiresorlapseswith outa CIdiagnosis. Levelpremiums aret ypicallypaid monthlythroughout theterm, thoughtheyma yceaseat, say ,

75 fora longterm policy .

Critical illnessco vermaybe addedtoalife insurancepolicyas anaccelerated benetrider. In thiscase, thecritical illnessdiagnosis triggers thepa yment ofsomeorall ofthe deathbenet under thelife insurance,with somediscoun tingadjustmen tapplied insomecases.Where the full benetisaccelerated, thep olicyexpires onthe CIdiagnosis.Ifonly partof theb enetis accelerated, thenthe remainderis paidout whenthe poli cyh olderdies.

1.4 Chronicillness insurance

Chronic illnessinsurance pays abeneton diagnosisof achronicillness, denedas onefrom whichthe policyholder willnotre cov er,althou ghtheillnessdoesnotnecessarilyneedtob e terminal. Thei llnessmustbe sucientlysevere thatthepolicyh olderisno longerableto performt woormoreofthe ADLslisted inthe LTC insurances ection.The benet undera chronicillness policy ispaidasa lumpsum oras anann uity . Chronic illnessinsurance ist ypicallyadded toastandardlife insurancep olicyas anaccelerated benetrider, similarlyto thecritical illness case.

1.5 Hospitalindemnit yinsurance(HII)

Hospital indemnityinsurancepa ysthe policyholderalump sumeac htimethe policyhol deris admitted forhospital treatment. Theremayalso be adailystipend pay ableduringahospital stay.Otherb enetsma yincludepaymen tsforemergencyro omor outpatientvisitsthatdonot result ino vernightadmission. The purposeofhospital indemnity insurancediers fromstandardhealthinsurance, which providesreim bursementofhealthcosts.Hospital indemnity insuranceb enetsare av ailablefor 10 the policyholdertouse how ever shewants{forexample,to pay forchildcareortra vel costsfor visiting family.Inthe USAit canb eused tooset uninsuredcosts associatedwiththe hospital visit, forexample, ifthe policyholder's healthinsurance coverrequires thep olicyholderto pay some ofthe costsof therequired treatment 2. Premiums forHI Iincreaseeach year, sothepolicies areessentiallyshort termin nature .How- ever,the insurersma yguaran teerenewalup toage65,whic hmeansthatthe policyholder isnot subjecttoann ualmedical assessmentateac hrenew aldate, andalso thatthepremiumsshould bethe samefor ap olic yholder whohasalreadymadeseveralclaimsunderthep olicyas fora policyholderwho hasnot.

1.6 ContinuingCareRetirement Communities (CCRCs)

quotesdbs_dbs6.pdfusesText_12