Miami University Sprint Class

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1 Miami University Sprint Class Prewrk G t and read abut the actuarial prfessin. Week 1 Why d we need actuaries? Cmpanies sell prmises nt widgets. Lng-term nature. Tpic 1 Types f Insurance Life Life: Traditinal whle life, participating, dividend paying, nn-participating with varius payment ptins Term Universal life Variable life and variable universal Jint life first r secnd t die Individual r grup Annuities: deferred, immediate, deferred immediate, market value adjusted, variable Pensin Health: medical, Medicare supplement, disability incme, dread disease, critical illness, accident Casualty Aut: cllisin, liability, uninsured mtrists Hmewners: fire, liability, windstrm, water NOT FLOOD Renters Liability Errrs and missins Malpractice Medical Accident C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 1

2 Tpic 2 -- Types f Actuaries Sciety f Actuaries FSA ASA (www.sa.rg) Casualty Actuarial Sciety FCAS ACAS (www.casact.rg) American Academy f Actuaries MAAA (www.actuary.rg) Other cuntries Tpic 3 Emplyment fr Actuaries Insurance cmpanies Cnsulting Gvernment Scial Security, Medicare, IRS, Wrkers Cmp, State Insurance Departments Academia Tpic 4 Types f Actuarial Wrk Financial Prduct Tpic 4 Car insurance example Hmewrk G t the Sciety f Actuaries website and learn abut the different types f actuarial exams and the tpics n them. Then visit the Casualty Actuarial Sciety website and d the same. Tpic 1 Insurance Backgrund Week 2 Review Week 1 Take Hme Wrk Why buy insurance? Utility Curves Ttal Utility C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 2

3 Marginal Utility Risk Averse vs. Risk Seeking Example: Why wuld a persn pay mre than the expected lss fr insurance? Using: unifrm distributin, integratin Why sell insurance? Law f large numbers Shw lss distributin f individual vs. cmpany Shw why insurance cmpany risk decreases as number f plicy hlders increase (prf why variance f average lss fr insurance cmpany = σ 2 /n) Criteria f insurable risk Pure risk vs. Speculatin vs. Gambling Tpic 2 Prbability and General Insurance Discrete Jint Prbability Functins Prbability, Severity Calculate expected value and variance General Insurance Pricing Use car r hmewner s insurance Layer csts fr expenses and prfit Expand prblem fr underwriting & adverse selectin Expand prblem fr mral hazard, deductibles and cinsurance Shw hw deductibles reduce # f claims filed Shw hw cinsurance culd lead t smaller claim amunts? (mainly health insurance d I want t include in example?) Ptential take-hme tpics Give students a list f risks. Ask whether they wuld insure thse risks and why? Set up a pricing spreadsheet that calculates expected lsses fr varius risk classes. Include sme utlier lsses. Ask students what price they wuld charge and why? Give expenses fr underwriting (differing by class) and ask hw much underwriting the students wuld perfrm (and what they wuld charge). C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 3

4 Week 3 Tpic 3 Interest Thery Review Week 2 Take-hme Wrk Interest Accumulatin Future Values Interest Discunting Present Values Cmpund Interest Cmpund accumulatin Cmpund discunting Nminal Rates f Interest Nminal versus annual effective Bnd equivalent rates Annual Percentage Rate (APR) versus Annual Percentage Yield (APY) Gemetric Series Definitin: a series with a cnstant rati between successive terms Cnverging gemetric series Frmula fr summatin f cnverging gemetric series Annuity Definitin: series f payments made at equal intervals f time Present value f annuity as a cnverging gemetric series, in terms f and Future value f annuity Perpetuities Amrtizatin Interest paid at time Principal paid at time Rll-frward f a balance Ptential take-hme tpics Lan amrtizatin Cmparing financing ptins Tax effects Effect f lump-sum payments n lan balance Refinancing ptins Credit Cards Negative amrtizatin C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 4

5 Week 4 Tpic 4 Mrtality Review Week 3 Take Hme Wrk Prbability fr Age at Death (Intrduce frmulas and ntatin) Survival Functin Time Until Death Cnditinal prbability f death - t q x Life Tables Prbability f death q x Prbability f survival - p x Select and Ultimate Mrtality Table Tpic 5 Life Annuity Overview Actuarial Present Value Intrductin f Annuity Terminlgy Immediate vs. Due Annuity Certain SPIA pricing example Premiums Expenses Cmmissins Ptential take-hme tpics Prblems related t mrtality Prvide students a SPIA pricing spreadsheet Ask them t calculate apprpriate premium t charge Add expenses and cmmissins, nw slve fr new premium Sensitivity test mrtality - slve fr new premium C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 5

6 Week 5 Tpic 6 Life Insurance Overview Review Week 4 Take Hme Wrk Cmmn Types f Life Insurance Term Limited cverage perid 10, 20, 30 years Lw cst Return f Premium Optin Whle Life Permanent cverage Builds cash value (savings cmpnent) Lans May pay dividends Universal Life Permanent cverage Insurance and savings cmpnents are unbundled Nnguaranteed elements Flexible premium payments Riders Term Riders Accidental Death Benefit Accelerated Death Benefit Guaranteed Insurability Waiver f Premium Tpic 7 Life Insurance Pricing Frmulas and ntatin f Life Insurance Whle Life Insurance n-year Term Insurance Basics f life insurance pricing Premiums Death Benefit Decrements (Deaths and Lapses) Expenses and Cmmissins Prfit Intrduce a simple pricing mdel C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 6

7 Ptential take-hme tpics Prvide custmer need scenaris and ask student t a identify the best type f prduct Prvide students a Term pricing spreadsheet Calculate apprpriate premium t charge t break even Add prfit gal - slve fr new premium Add cmpetitive gal hw wuld assumptins need t change t achieve bth prfit and cmpetitive gals? C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 7

8 Week 6 Tpic 8 Reserves Review Week 5 Take Hme Wrk Basic Accunting Balance Sheet Assets Liabilities Equity Incme Statement Revenue Expenses Operating Gain and Net Incme Example: Insurance cmpany financial statements What is a Reserve? Regulatry Perspective Claims-paying ability Amunt set aside t pay future bligatins Accunting Perspective Matching revenue with expense Illustratin: Premium vs. Mrtality slpe Basic Reserve Calculatins Fundamental Equatin: PVFB PVFP Checking accunt Example Net Premium Methd Tpic 9 Pensins Pensin Plan Basics Defined Benefit Plan Defined Cntributin Hybrid Plans Cash Balance Plans Defined Benefit Plan Valuatin Liability (Obligatin) Definitins Pensin Benefit Obligatin (PBO) Accumulated Benefit Obligatin (ABO) Vested Benefit Obligatin (VBO) Cmpnents f Obligatin Current Service Cst Interest Cst Past (Prir) Service Cst C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 8

9 Changes in Actuarial Assumptins discunt rate mrtality prjected salary grwth rate emplyee turnver rate Benefits Paid Basic Pensin Benefit Obligatin Calculatins Relate t annuity calculatin (PV f future payments) prject payments effects f changing actuarial assumptins Pensin Benefit Obligatin Rll Frward Ptential take-hme tpics Incrprate reserves int pricing example frm week 5 Calculate pensin liability. Calculate the change in the liability frm ne perid t the next, invlving the pieces (rll frward). Current service cst and Interest cst are guaranteed changes (happen every perid), and are calculated directly. Analyze the impact f changes in the varius actuarial assumptins t determine an actuarial (gain)/lss. Have them analyze the impact f a plan amendment t determine the prir service cst. C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 9

10 Week 7 Tpic 10 Current Events Scial Security Issues Medicare & Medicaid Issues Current Regulatry Issues Actuaries in the News C:\ByranSmucker\Teaching\Miami\ Spring-STA271\syllabus.dcx Page 10

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