Chapter 1: Why Insurance? How insurance works: insured transfer risiko ke insurer, insurer dpt premium. Melalui serangkaian perhitungan, insurer akan dpt average risk lbh rendah dibandingkan original risk tiap policyholder. Ini adlh akibat dr law of large numbers
2 1 1 2 2 =( +⋯+) = 2 =
Insurance and utility – premi hrs memenuhi:
r.v besar loss, averse)
[ℎ−] ℎ−] = [ℎ− ℎ− ] ′′′ ><00
utility function yg memenuhi decreasing marginal utility of money (risk
What makes a risk insurable: 1. Economically feasible – utility gained bs meng-cover biaya” spt komisi penjualan, expense kantor, dll. 2. Calculable economic value – cth ‘ya’: asuransi tabrakan mobil, datanya tersedia banyak. Cth ‘tdk’: asuransi nuclear meltdown: tdk ada data yg banyak, ditanggulangi dg perjanjian risk sharing. 3. Definite loss – mencegah manipulasi & moral hazard. Cth ‘definite’: kecelakaan mobil dg surat polisi, kematian. Cth ‘tdk’: disability, krn tdk jelas kriteria bs kembali bekerja dan bagaimana memantau malingering. 4. Random loss in nature – yg diasuransikan adlh kejadian yg diluar control policyholder. 5. Homogeneous exposure in any rate class – expected loss tiap unit di suatu kelas hrs sama dg expected loss sembarang unit di kelas tsb. Ini bs tdk terpenuhi dlm kasus anti-selection by policyholder, i.e. policyholder py lbh banyak informasi drpd insurer, yg lalu dimanfaatkan utk price advantage. 6. Spatially & temporally independent exposure units – claim suatu policyholder tdk mempengaruhi claim policyholder lain. Insurance from policyholder pov tdk menghslkan profit. Dlm speculation ada transfer risk ke speculator, dimana motive dr speculator adlh peluang menghslkan profit. Dlm gambling risiko
diciptakan. Risk : ukuran variabilitas antara actual & expected outcome. Peril: alat utk mengidentifikasi cause of risk. Cth: kebakaran, tabrakan, [encurian, bencana alam, dll. Hazards: factor” yg berkontribusi pd peril. Cth: lokasi, struktur, moral hazard spt ketidakjujuran dll. Other reasons membeli asuransi:
1. 2. 3. 4. 5.
Legal requirements Lenders’ requirements Commercial requirements Special expertise Taxation
Chapter 2: Property/Casualty Coverages Automobile insurance 1. Section A / liability ins / third party liability / BI/PD (bodily-injury/property damage) –
Provides coverage to the PH jk, sbg sopir dr kendaraan yg dicover, PH melukai pihak ketiga atau merusak properti pihak ketiga. Properti PH tdk dicover oleh asuransi ini. 2. Section B / medical benefits / medical payments (tort) / personal injury protection (nofault) / accident benefits (Canada) – Provides coverage to the PH & family thd injury dr kecelakaan yg disebabkan oleh PH atau kecelakaan apapun di yurisdiksi no-fault. 3. Uninsured & underinsured motorist coverage – Provides protection for the PH & family jk terluka oleh unidentified/uninsured/underinsured motorist. 4. Section C / collision & other than collision (OTC) ins – Insurer membayar kerugian atas kerusakan kendaraan PH dlm kecelakaan, biasanya ada deductible. Subrogation (tort): jk another driver yg bersalah, insurer bs menuntut ganti rugi cost-nya dan jg deductibles utk PH. Mekanisme ini menurunkan premi collision ins dan menaikkan premi liability ins. Salvage: jk collision claim requires paying the full value atas kendaraan, maka sisa” kendaraan tsb jatuh ke kepemilikan insurer (salvage value). Jk salvage value > pembayaran insurer ke PH, insurer hrs tambah pembayarannya setdknya sebsr selisihnya (insurer tdk bs dpt profit dr salvage provision). OTC: hail fire, vandalism, stone chips, theft, dll, kecuali war, act of terrorism, due to wear & tear, road damage to tires, radioactive contamination, due to discharge of nuclear weapon, and collision. Jk coverage diberikan utk semua listed tsb kecuali yg diexclude maka disebut comprehensive coverage. Jk hy bbrp maka disebut specified perils. All risk coverage: gabungan collision & OTC. Umumnya 2 pertama diwajibkan oleh hukum yg mensyaratkan pemilik kendaraan utk membeli asuransi yg memenuhi financial responsibility limits. Tipe” legislation defining auto ins benefit: Tort/at fault system: benefit dikeluarkan hy jk insurer percaya bhw insured-nya bersalah atas kecelakaan terkait atau jk pihak yg terluka menuntut & membuktikan bhw insured bersalah. Umumnya small claims jd highly overcompensated dan small claims hy dikompensasi 30% dr biaya sehrsnya. Terlebih, hy 25% premi yg akhirnya sampai di pihak terluka, sisa 75% masuk ke biaya pengadilan dll. No fault system: pihak terluka tdk perlu menuntut ataupun membuktikan pihak lain bersalah atas kecelakaan terkait. Benefit akan dibayarkan oleh injured party’s own insurer. Premi jd jauh lbh murah krn mengeliminasi legal fees dll. Threshold no-fault : look first to no fault system (own insurer). Jk injuries melebihi threshold, maka bs tempuh tort settlement.
Homeowners insurance 1. Coverage A – proteksi thd kerusakan akibat perils tertentu atau dg basis all-risk dg limit
tertentu. Doctrine of proximate cause: suatu kerugian dicover hy jk covered peril is the proximate cause of a covered sequence, yaitu jk peril tsb menginisiasi suatu unbroken sequence of events yg mengakibatkan covered consequence. Biasanya ada deductibles utk exclude klaim” kecil yg tdk ekonomis atau mahal di biaya administrasi, jg mendorong policyowner lbh responsible. Ada mekanisme subrogation, misal kebakaran akibat wiring problem, pihak asuransi bs tuntut ganti rugi ke perus wiring. Coinsurance: asuransi membayar suatu bagian dr kerugian. Jk asuransi lbh bsr sama dg 80% nilai rumah pd waktu kerugian, maka asuransi tsb dianggap asuransi utk full value:
=min{, 0.8 ×}
insurance for loss ,
sum insured, dan
full value.
(-) Konsepnya tdk mudah dimengerti Policyholder yg beli asuransi less than full coverage hy dipenalti jk tjd claim. Coinsurance 80% atau persen brppun di bawah 100% mendiskriminasi org” yg beli higher level of insurance, pdhl sehrsnya ini diencourage Tingginya inflasi nilai real estate membuat homeowner scr tdk sadar jatuh di bwh coinsurance % Penggunaan coinsurance <100% scr tdk lgsg merekomendasikan policyowner utk beli asuransi less than full coverage. Mslh inflasi diatasi insurer dg menaikkan limit tiap tahun utk mengejar inflasi. Coverage B – memberikan specific amount of ins thd garage atau struktur lain yg terpisah dr properti utama, umumnya senilai 10% dr coverage properti utama (bs lebih dg premi lebih). Coverage C – insure the actual cash value of the policyholder’s personal property & isinya up to a defined policy limit, umumnya 40-50% insured value of the house. Inside limit for certain losses: limit penggantian utk barang tertentu. Misal kasus pencurian atau hilang cash. Misal insureds ingin full insurance atas perhiasan, silverware, atau barang seni, maka dibuatlah schedule (extra premium apply). Kasus kerugian atas ketiga barang tersebut akan diganti sesuai nilai yg tercantum di schedule, bukan sesuai nilai pasarnya saat itu. Benefit ini disebut valued benefit krn tdk ada loss distribution utk hal ini. Coverage ini jg berlaku ketika personal items tsb berada di luar rumah, misal saat traveling. Coverage D – provides coverage for additional living expense & loss of rental income. Asuransi ini membayar fair rental value of alternative accommodation saat properti sedang diperbaiki akibat kerusakan dr covered peril. Umumnya limitnya 20% dr coverage propertinya. Liability coverage – coverage atas liability yg muncul ketika third party terluka atau jk properti third party rusak saat sdg berada di properti PH atau keadaan tertentu. Spt auto ins, insurer bd defend PH di persidangan.
(+) Encourage insurers to value by penalizing under insurance Premi lbh adil. Jk loss skewed to smaller claims tp premi berbanding lurus dg nilai asuransi, tanpa coinsurance, org dg asuransi lbh kecil jd lbh berisiko bg insurer. The overall rate level can be lower but still adequate. Ini akibat dr poin 2, krn tiap org bayar sesuai risikonya.
2. 3.
4.
5.
Tenants package – utk PH yg menyewa, bukan memiliki rumah sendiri. Mengcover hampir semua di
homeowners ins tp disesuaikan. Misal jk gedung apartemen rusak krn kebakaran dll, concern tenants hy barang pribadinya saja. Workers compensation – workers gave up their rights to sue their employers terkait occupational
accident or sickness in return for a no-fault benefits on a pre-defined or scheduled basis. Sblm 1895, workers hrs menuntut employer-nya utk dpt kompensasi, lalu terbentur kesulitan berikut: Doctrine of contributory negligence: worker turut berkontribusi atas tjdnya injury/sickness Fellow-servant doctrine: injury/sickness disebabkan oleh fellow-worker Assumption-of-risk doctrine: worker sdh tahu bahaya yg terkandung dlm pekerjaan tsb Tujuan dr workers compensastion: Perlindungan menyeluruh atas occupational injury/disease Proteksi substantial atas loss of income Medical care & rehabilitation service yg memadai Encouragement of safety An efficient & effective delivery system for benefits & services Umumnya worker dpt compensastion benefits berikut: Medical care Disability income. Degree of disability: (1) temporary but total, (2) permanent & total, (3) temporary & partial, (4) permanent but partial. Death benefits. Includes biaya pemakaman dan cash-income payments to dependents tertentu. Rehabilitation services & benefits
Benefits dibayar oleh insurer atau employers yg ‘qualified self -insurers’. Fire insurance 1. Fire ins – proteksi atas kerugian/kerusakan bangunan & personal property akibat fire,
lightning, windstorm, hail, explosion, dll. Coverage provided for direct loss (kerusakan properti) & indirect loss (loss of income atau extra expenses akibat loss of use of the property). 2. Standard fire policy (SFP) – hy cover direct loss akibat fire & lightning, dan setdknya satu additional form berikut hrs attached utk dpt valid policy: Those that provide personal coverage (dwelling building & contents forms) Those that provide commercial coverages (general property, multiple location, & reporting forms) Those that increase the covered perils, misal extended coverage utk vandalism, dll. Those that increase the covered loss, misal additional living expenses, rental value, dll. Jenis” perlindungan yg dibuat oleh fire insurers pd polis terpisah, bukan sbg forms attached to the SFP, disebut sbg allied lines.
Marine insurance 1. Ocean marine ins – proteksi thd financial loss krn kerusakan owned property akibat perils
terkait transportasi. Mengcover slrh tipe oceangoing vessels & kargonya. 2. Inland marine ins – utk trucking industry, modifikasi marine ins. Liability insurance
Provide 2 levels of security for the PH: 1. Dlm kasus injury to a third party atau kerusakan property third party, dan PH dituduh bersalah, insurer akan defend PH di pengadilan, tp bs stop defense tsb jk biaya atas kerusakan sdh melebihi limit. 2. Further, jk PH terbukti bersalah, insurer bayar kerugian hingga limit. Cth liability ins terjual terpisah: product liability ins, errors & omissions ins, medical malpractice ins, professional liability ins, dll. Coverage ini dicirikan oleh Low claim freq but high value claims yg umumnya direport bertahun” stlh occurrence dan butuh bbrp tahun lg utk diselesaikan. Ini diatasi dg dibuatnya claims-made policy, yaitu claim yg dicover hy claim yg tjd di periode polis, tdk peduli kapan penyebabnya tjd. Polis tsb dpt dilengkapi tail coverage, yakni mengcover claims yg terjadi di periode tail atas penyebab yg terjadi di periode polis. Potential for high litigation cost. Diatasi dg policy limit yg membatasi both defense cost & indemnity payment.
Limits to coverage 1. Deductibles
(+) Small loses do not create claim, jd menghemat expenses Utk larger losses, avg claim payment is reduced by deductible which is translated into premium savings Deductible puts the PH at risk, shg memberi insentif bg PH yg mencegah tjdnya klaim PH dpt mengoptimalkan utility uangnya dg higher deductible (lower premium). Dg kata lain, lbh bernilai utk mengurangi premium drpd utk mengurangi
(-) Insured kecewa krn losses not paid in full Can lead to misunderstandings & bad public relations Marketing jd sulit Insured bs inflate claim utk recover deductible. Jd tdk adil bg honest PH who will pay the resulting higher premium.
deductible utk cover small loses yg tdk terlalu bernilai. Bbrp tipe deductible: a. Fixed dollar apply to each claim. b. Fixed percentage of loss atau policy limit that apply to each claim. Biasanya dikombinasikan dg (a) spy insurer tdk perlu handle small claims. c. Disappearing: loss
b pays full, an insurer pays full. biasanya di ocean marine ins. e. Fixed dollar deductible per calendar year (instead of per loss), biasanya di health ins atau medical expense ins. f. Elimination period: jeda waktu antara time of the disablement to the date that disability benefits begin. 2. Policy limits Reasons: To clarify the insurer’s obligation. Memberi upper bound distribusi kerugian bagi insurer. Allows the PH to choose appropriate coverage at an appropriate price.
Chapter 3: Ratemaking Objectives 1. Essential Cover expected losses & expenses – income (premi & inv income) setdknya sebesar
pengeluaran. Produce rates that make adequate provision for contingencies – such as unexpected losses (cth: 100-year flood, dll). Jk terlalu ti nggi bs kalah saing. Jk terlalu rendah, terpaksa nombok dr surplus, akibatnya mengurangi kesempatan utk expand bisnis, jg mengurangi solvency insurer. Encourage loss control – desain proses klasifikasi risiko yg baik dpt memberikan insentif ekonomi yg bsr bg PH yg berupaya mengurangi klaimnya. Cth: diskon utk good driver di auto ins, diskon utk sprinkler system & burglar alarms in homeowner ins. Ada nilai sosialnya jg dlm hal mengurangi kecelakaan. Satisfy rate regulators – scr umum persyaratannya adlh premi hrs cukup. 2. Non-essential but desirable Produce rates that are reasonably stable – efek bencana alam besar ke premi hrs disebar spy tdk perlu tiba” menaikkan premi cukup besar. Reinsurance jg bs membantu disini. Produce rates that are reasonably responsive to changes – bs beradaptasi dg perubahan” yg memiliki immediate atau long-term consequences. somehow kontridiksi dg poin sblmnya. Be simple & easy to understand – memudahkan agen & broker utk menjual produk. Jk fitur produk rumit maka Ph akan sulit merelate antara loss control & lower rates, encouraging loss control jd sulit.
Inputs
1. Claim freq dist . Avg claim freq:
= #
Perhatikan kemungkinan loss occur tp tdk menyebabkan claim (cth: loss
= = # = +
3. Rate ( ) / force ( ) of interest 4. The times at which the payments are made. Loss cost per unit exposure/pure premium/net premium:
= × =
Variance dr expected value umumnya berasal dr survival model & rate of interest (utk life ins & pension plan) atau claim freq & loss dist (utk property/casualty ins). Data
Paid losses is the total loss payment Data lengkap stlh
Accident Year (AY) Z
Policy Year (PY) Z
Calendar Year (CY) Z
Atas kejadian yg tjd di CY Z Slrh loss di AY Z dibayar. Di awal” sangat bergantung pd perhitungan rsv.
Atas kejadian dr polis” yg issued di CY Z Maks 24 bulan, krn bs ada polis yg issued di 31 Des Z
Yg dilakukan di CY Z 1 tahun
Written premium: cash accounting. Earned premium: amounts actually earned in the period (accrual accounting).
=+
Premi dihitung sbg rate/unit dikali unit exposure. A good exposure unit base: Ukuran akurat atas quantitative exposure to loss Mudah ditentukan oleh insurer (pd waktu dihitungnya premi) Tdk dpt dimanipulasi insured Easy to record & administer Dipahami PH Scr automatis menyesuaikan dg biaya penyelesaian klaim.
Expected effective period: periode terjadinya loss yg mungkin tjd di bawah polis” yg diterbitkan dg
new rates. Ada jeda antara experience period dg calculation date dg effective date (waktu start expected effective period), shg bs mempengaruhi keakuratan perhitungan new rates. AY PY CY More common, bs pakai most Mempertimbangkan hub antara Jarang digunakan di recent data & perhitungan loss- klaim & premi yg terkumpul. ratemaking development factors. Data Tp data tdk lengkap hingga 31 claim umumnya dlm format AY, Des Z+1, jd antara hrs pakai jd lbh ready estimasi atau data yg outdated Ingredients of ratemaking 1. Loss development factors – menunjukkan pertumbuhan total paid loss dr waktu ke waktu.
Utk mengestimate complete loss data dari latest loss data (dlm format loss triangle, i.e. data total paid loss). Incurred loss-development factor bs <1: a. Perhitungan rsv yg konservatif (ultimate loss akan < rsv). b. Adanya recovery dg & subrogation. Distorsi dr large losses diatasi dg batas atas loss atau merata”kan large loss over a longer period of time. 2. Trend factors – utk mengestimasi expected loss cost di masa mendatang, dg cara meng’adjust’ past experiences ke future levels. Ini utk mengcater cost changes akibat inflasi, benefit, dll. Misal dg analisis regresi, baik linier maupun logaritmik:
= ×
Dlm menginput perhatikan data. Jk pakai AY data maka avg accident date adlh 30 Jun Z, jk PY maka 31 Des Z. Maka projectednya jg utk waktu avg tsb. Hrs adjust dg interpolasi utk dpt estimate di titik waktu lain. Dlm mengestimasi, perhatikan jg fator” luar lain: Recent court adjudication’s Interpretation of recent legislative changes Expected change in the rate of economic inflation Level of economic activity Recent changes in underwriting criteria or definitions Changes in mandated benefit levels 3. Expenses a. Loss adjustment expenses (LAE): biaya terkait loss adjustment & payment process: Allocated loss adjustment expenses (ALAE): LAE yg dpt diasosiasikan dg suatu claim, umumnya memiliki sifat” yg mirip dg losses shg serigkali dikombinasikan dg losses utk ratemaking. Cth: lawyers’ fees. Unallocated loss adjustment expenses (ULAE): tdk dpt diasosiasikan dg suatu claim. Dimasukkan ke incurred loss dg formula lain. Cth: gaji pegawai. b. Expense yg mencakup komisi, premium taxes, licenses & fees, head office expenses. Umumnya dinyatakan sbg % of gross rate.
= ℎ ℎ , % =1− & =
Bbrp insurer memisahkan expense menjadi variable (V) yg bergantung pd gross rate & fixed (F) per unit exposure
& + = 1−
4. Loading for profit & contingencies Implicit approach: menggunakan conservative input parameters & methodologies dlm perhitungan premi. Harapannya agar actual lbh baik dr expected shg dihslkan profit. Explicit approach: menghitung premi dg basis best estimate (tanpa level of conservatism), lalu menambahkan explicit factor (umumnya % of gross rate) utk profit & contingencies. Lbh popular digunakan. 5. Credibility factors Z – alat utk compromise between responsiveness & stability when working with sparse data. Merupakan fungsi dr ketidakpastian terkait underlying freq & severity dist. Properties: . Fully credible . , yakni volume of experience data ↑ maka credibility ↑.
0≤ ≤ 1 > 0 < 0
=1
, yakni size of the risk ↑ maka % change in credibility ↓.
2 formula credibility yg umum:
,>0 = + =min√ ,1
Dg E ukuran exposure (cth: premium income), K konstanta utk mencerminkan variability of business, n ukuran exposure (cth: # claims), k # claims yg dibutuhkan utk full credibility. 6. Investment income – hrs memperhitungkan time value of money. Misal premi utk $1mn liability loss hrs lbh kecil jauh drpd utk $1mn fire loss, krn the former takes several years to settle. Rate changes steps: 1. Overall avg rate change 2. Changing risk classification differentials 3. Balancing back
