Riba:
- Ability don kafa triangle ci gaban lalacewa, IBNR (lalacewar da aka samu amma ba a ba da rahoto ba) da hanyar sarkar-tsani tare da tallafin fasaha na wucin gadi da fassara abubuwan haɓakawa.
- Ikon kwatanta sakamako tare da wasu hanyoyin kamar Bornhuetter-Ferguson da Mack da bayyana rashin tabbas (sauyi, tazarar amincewa) tare da hankali na wucin gadi.
- Samun ikon kiyaye cewa adadi na tanadin da aka lissafta ta hanyar basirar wucin gadi shine daftarin, ba na ƙarshe ba, kuma cewa zaɓin abubuwan haɓakawa da gyaran shari'a na da alhakin aikin.
Lokacin da kamfanin inshora ya biya don lalacewa a yau, hakika yana biyan bashin manufofin da ya sayar a baya. Amma ba kowane lalacewa ba ne nan da nan aka bayar da rahoton ba kuma ba kowane barnar da aka bayar ba ne ake biya cikakke nan take. Wani hatsarin mota ya faru a yau, an sanar da kamfanin bayan watanni uku, aikin kotu yana ɗaukar shekaru biyu, kuma biyan kuɗi na ƙarshe ya bayyana bayan shekaru huɗu. Don haka, dole ne kamfani ya tanadi kuɗi a yau don diyya waɗanda ba a biya su gabaɗaya ba ko ma ba a ba da rahoto ba tukuna. Ana kiran wannan kuɗin ajiyar kuɗi, kuma ingantaccen lissafinsa shine mafi mahimmancin aikin kamfanin inshora. Idan ya bar ƙasa kaɗan, kamfanin zai shiga fatara; Idan aka ware da yawa sai a daure babban jari a banza kuma a boye ribar da aka samu.
A cikin wannan rukunin, za mu rufe ra'ayoyi guda uku a cikin zuciyar samar da lissafin kuɗi: triangle ci gaban lalacewa, IBNR da hanyar sarkar-tsani. Sa'an nan kuma za mu yi la'akari da wasu hanyoyin (Bornhuetter-Ferguson, Mack) da rashin tabbas. AI yana rubuta lambar don waɗannan ƙididdiga, ya cika triangle, ƙididdige abubuwan kuma ya bayyana sakamakon; amma alhakin zaɓin abubuwan haɓakawa, gyaran shari'a da adadi na ƙarshe ya ta'allaka ne ga mai aiki.
Menene triangle ci gaban lalacewa?
Tushen lissafin tanadi shine triangle na ci gaba / kashe-kashe triangle. Layukan suna nuna lokacin da lalacewar ta faru (shekarar haɗari), kuma ginshiƙan sun nuna nawa aka biya don wannan lalacewa (shekarar ci gaba). Ya kasance kamar haka: An biya miliyan 4 a shekara ta farko ta ci gaba na shekarar 2021, an biya jimlar miliyan 6.2 a shekara ta 2, kuma an biya miliyan 7 a shekara ta 3rd. Tsofaffin shekarun haɗari sun girma (kusan duk an biya su), yayin da sabbin shekarun ke ci gaba. Saboda haka sunan triangle: ƙananan kusurwar dama ba ta da komai, saboda ci gaban ci gaba na sababbin shekaru bai riga ya faru ba. Aikin mai wasan kwaikwayo shine kimanta wannan kusurwar mara komai.
IBNR (wanda aka jawo amma ba a ba da rahoto ba) yana cikin ainihin ɓangaren wannan gibin: farashin da'awar da aka yi a gaba wanda ya faru amma har yanzu ba a kai rahoto ga kamfanin ba. Akwai kuma IBNER (ƙarin ci gaban da aka ruwaito amma rashin tanadi). A aikace, hanyoyin triangle suna ƙididdige yawan tanadin da ake buƙata (biya + ci gaban gaba); Lokacin da ka cire rabon da aka biya, ragowar tanadin ya ragu, gami da IBNR.
Tukwici: Kuna iya saita triangle akan tushe guda biyu: "lalacewar da aka biya" da "lalacewar da aka samu (wanda aka biya + sanannen ajiyar kuɗi)". Yin nazarin waɗannan biyu tare yana taimaka muku kama canjin halin yin rajistar ƙungiyoyin da'awar.
Sarkar-tsani mataki-mataki
Tsanin sarkar ita ce hanyar mayar da martani da aka fi sani, kuma hikimarsa tana da hankali: idan hasarar da aka yi a baya ta yi girma a wani matsakaicin matsakaici daga shekara guda na ci gaba zuwa gaba, sabbin shekaru za su yi girma a daidai wannan adadin. Matakai:
- Saita tarin triangle. Tsara jimlar da'awar biyan kuɗi na kowane haɗari shekara zuwa shekara na ci gaba.
- Kididdigar abubuwan ci gaba. Ga kowane ginshiƙi wucewa: jimlar shafi na gaba / jimlar shafi na yanzu (amfani da layuka kawai waɗanda ginshiƙan biyu suka shagaltar). Misali, ma'aunin 1→2 shine 1.45; Matsakaicin 2→3 na iya zama 1.12. Ana kiran wannan al'amari na shekaru-zuwa-shekara.
- Nemo abubuwa masu tarawa ( stacked). Haɓaka sauran abubuwan da suka rage don kaiwa wasan karshe na kowace shekara.
- Cika kusurwa mara kyau. Yi ƙididdige lalacewa ta ƙarshe ta hanyar ninka ƙimar da aka sani na ƙarshe na kowace sabuwar shekara ta haɗari da sauran abubuwan.
- Yi lissafin amsa. Lalacewar ƙarshe - biya har zuwa yau = tanadin da za a biya a nan gaba (ciki har da IBNR).
Tebur mai zuwa ƙaramin misali ne (lalacewar da aka biya ta tara, miliyan TL):
shekarar hatsari
Ku zo. 1
Ku zo. 2
Ku zo. 3
Ku zo. 4
2021
4.0
6.0
6.8
7.0
2022
4.4
6.5
7.3
?
2023
4.8
7.0
?
?
2024
5.2
?
?
?
A cikin wannan alwatika, adadin 1→2 shine kusan 1.47; 2→3 game da 1.12; 3→4 yayi daidai da 1.03. 2024 na ƙarshe 5.2 × 1.47 × 1.12 × 1.03 ≈ 8.82 miliyan; Tunda adadin da aka biya shine 5.2, tanadin shine ≈ 3.62 miliyan TL. AI yana yin wannan lissafin a cikin daƙiƙa, amma mai yin aikin ya yanke shawarar ko abubuwan suna da ma'ana.
Madadin hanyoyin da rashin tabbas
Tsanin sarkar kadai bai isa ba saboda abubuwan ci gaba suna da matukar damuwa ga ƙananan sauye-sauye saboda akwai ƙananan bayanai a cikin 'yan shekarun nan na haɗari; Babban lalacewa ɗaya na iya busa duk ƙiyasin. Shi ya sa ake amfani da hanyar Bornhuetter-Ferguson (BF): BF tana ƙididdige ɓangaren da ba a haɓaka ba ta hanyar amfani da bayanin rabon asarar da ake tsammani na waje kuma ta haka yana sassaukar da ƙarfi. An fi son tsanin sarkar a cikin shekaru masu girma, BF an fi son shi a cikin sababbin shekaru da balagagge; Tare suna ba da ma'auni ma'auni.
Don auna rashin tabbas, ana amfani da hanyar Mack: yana ba da daidaitaccen kuskure (sauyi) na ƙididdigar ma'aunin sarkar. Bugu da ƙari, ana iya samar da cikakken yiwuwar rarraba amsa ta hanyar bootstrap (kwaikwaya ta hanyar yin amfani da bayanan akai-akai); Wannan yana amsa tambayar (mai mahimmanci ga Solvency II) na "menene martaninmu zai kasance a cikin mafi munin yanayi?" AI yana da ƙarfi sosai wajen samar da lamba da kwatanta waɗannan hanyoyin.
Tsanaki: Zaɓin abubuwan haɓaka ba inji bane. A cikin shekara guda, canje-canje a cikin doka, yawan ƙararraki, ko canjin adadin biyan kuɗi na iya rushe abubuwan. Zaɓin "matsakaici mai sauƙi, matsakaicin nauyi, shekaru 3 na ƙarshe" na shari'a ne kuma dole ne ya zama barata.
Yadda ake amfani da AI a cikin lissafin ajiya
1) Lambar tsani:
Rubuta lambar sharhi a cikin Python wanda ke ƙididdige tsanin sarkar. Shigarwa: tarin triangle na lalacewa (jerin jeri, bacewar sel Babu). 1) Yi ƙididdige ma'auni mai nauyin girma don kowane wucewar shafi. 2) Nemo abubuwan tarawa. 3) Cika a cikin kusurwoyi mara kyau kuma kimanta lalacewa ta ƙarshe ga kowace shekara ta haɗari. 4) Yi ƙididdigewa da jimlar diyya (na ƙarshe - biya). Buga kowane matsakaicin mataki zuwa allon; kar a gyara ɗakin karatu, yi amfani da Python na asali.
2) Kwatancen hanyar:
Bayyana wa ɗan wasan kwaikwayo bambanci tsakanin tsanin sarkar da Bornhuetter-Ferguson.- Wanne ya fi dogara a cikin wane yanayi? - Me yasa aka fi son BF a cikin sababbin shekaru masu haɗari? - Ta yaya zan ƙayyade 'lalacewar lalacewa' da ake bukata don BF? Takaita fa'idodi/kissoshi a cikin tebur.
3) Tabbatar da ingancin dalilai:
Ina da abubuwa masu zuwa na shekaru: 1->2: 1.47; 2-> 3: 1.12; 3-> 4: 1.03; 4->5: 1,45.The 4->5 factor ya dubi m idan aka kwatanta da sauran.- Menene zai iya zama yiwu dalilai na wannan tsalle (ka'ida, manyan lalacewa, data kuskure)? - Menene cak ya kamata in yi don tabbatarwa? Yanke yanke shawara; Ka ba ni lissafin lissafi.
4) Tafsirin rashin tabbas:
Tsani na mafi kyawun zato shine TL miliyan 42, kuskuren daidaitaccen Mack shine miliyan 5.3. Ta yaya zan bayyana wannan ga manaja da mai gudanarwa? - Bayyana a cikin harshe bayyananne abin da matakan 75% da 99.5% ke nufi. - Ta yaya zan iya isar da saƙon 'kewaye maimakon lamba ɗaya'?
Rauni mai ƙarfi / Ƙarfi mai ƙarfi
Rawanin faɗakarwa:
Yi lissafin ladana.
Babu triangle, babu hanya, babu bayanai. AI ya dace da gibin.
Ƙarfi mai ƙarfi:
Matsayin ku: mataimakiyar ajiyar kuɗi. Zan ba ku jimlar da'awar da'awar alwatika (wanda ba a san shi ba, miliyan TL): 2021: [4.0, 6.0, 6.8, 7.0] 2022: [4.4, 6.5, 7.3]2023: [4.8, 7.0]2024: [5.2] Ɗawainiya-daukar nauyin shekaru: 1. Cika ɓangarorin da ba kowa, rubuta asarar ƙarshe na kowace shekara.3) Ƙididdige jimillar tanadi (na ƙarshe - biya).4) 2024 sabon abu ne; Don haka bayyana dalilin da yasa ƙimar ku ta fi rashin tabbas. Nuna mani matsakaicin lambobi don in tabbatar da su da hannu. Kawai amfani da bayanan da na ba ku.
uku mini lokuta
Case 1 - Rashin wadataccen tanadi. Wani kamfani ya ƙididdige shekarun haɗari biyu na ƙarshe a cikin babban fayil ɗin zirga-zirgar zirga-zirgar sauri tare da madaidaicin tsani. Tun da sababbin abubuwan 'yan shekarun sun yi ƙasa, an kiyasta tanadin a miliyan 31 TL. Lokacin da actuary ya bincika tare da BF kuma yayi amfani da ƙimar lalacewa da ake tsammani, ainihin martanin shine 44 miliyan TL. Bambanci na miliyan 13 an tabbatar da shi tare da ainihin lalacewa a shekara guda. Darasi: a cikin sababbin shekaru, sarkar kawai tana yaudarar tsani.
Case na 2 - Fasali na lalacewa. Mataimakin actuary ya ga 3→4 factor na 1.42 a cikin triangle wanda AI ya samar; yayin da matsakaicin tarihin ya kasance 1.05. Idan da ta wuce ba tare da tambaya ba, da martanin zai yi tashin gwauron zabi da kusan kashi 30 cikin dari. Binciken ya nuna cewa shekaru biyu na haɗari sun canza saboda kuskuren loda bayanai. AI bai haifar da kuskure ba, amma bai lura da shi ba; An ci gaba da bincikar hankalin ɗan wasan.
Case 3 - Daidaita gabatar da rashin tabbas. Wani jami'in da ke da alhakin ya gaya wa gudanarwa kawai cewa " tanadar shine miliyan 42." Hukumomin sun yi tunanin wannan ya tabbata kuma sun rarraba riba. A shekara ta gaba, lokacin da ainihin adadi ya kai miliyan 48, rikici ya taso. Lokaci na gaba, wasan kwaikwayon ya ba da kewayon tare da Mack da bootstrap yana cewa "mafi kyawun zato shine 42, amma matakin 75% shine 46, matakin 99.5% shine miliyan 55"; Hukumar gudanarwa ta yanke shawarar yadda ya kamata. Ya adana lokaci mai yawa don shirya lambar AI bootstrap da ginshiƙi.
Kuskuren gama gari
- Yin amfani da matakan sarkar kawai a cikin 'yan shekarun nan na hatsarori. Ƙananan bayanai yana nufin abu maras tabbas; Balance da BF.
- Rashin ƙaddamar da abubuwan haɓakawa ga kula da hankali. Wani lalatacciyar al'amari ya kawar da duk amsa; Kwatanta da tsarin tarihi.
- Gabatar da ma'amala azaman ainihin lamba ɗaya. Amsa ita ce zato; Gabatar da shi ba tare da kewayon rashin tabbas ba (Mack, bootstrap) yaudara ne.
- Rikita triangle da aka biya kuma aka gane. Biyu suna auna abubuwa daban-daban; Yi aiki akai-akai akan tushe ɗaya ko kwatanta su da sane.
- Yin watsi da hauhawar farashin kayayyaki da raguwar tsari. Tsarin ci gaban da ya gabata bazai kasance iri ɗaya ba a nan gaba; Hakanan la'akari da canjin tsari.
A takaice
Ajiye shine ƙididdigar halin yanzu na abin alhaki na gaba kuma shine mafi mahimmancin lissafin aikin kamfanin inshora. Ana ganin tsarin biyan kuɗi na baya tare da triangle na ci gaba; Tsani na sarkar ya cika kusurwar da ba komai tare da dalilai na shekaru-da-shekara kuma yana kimanta lalacewa ta ƙarshe da ramuwa ciki har da IBNR. A cikin sababbin shekaru, BF ya fi kwanciyar hankali; Ana auna rashin tabbas ta Mack da bootstrap. AI ya cika cikin triangle, ya rubuta lambar, kuma yana kwatanta hanyoyin; amma zaɓin dalilai, duban hankali da adadi na ƙarshe ya dogara da hukunci da sa hannun mai aiki.
Aikin aikace-aikace
Ƙirƙirar ƙaramin triangle mara suna na ƙididdigar biyan kuɗi (shekarun haɗari 4 × har zuwa shekarun ci gaba 4). Tambayi AI don lissafta daidai da tsanin sarkar. Da hannu tabbatar da abubuwan shekaru-da-shekara da ƙarshen shekaru 2. Sa'an nan kuma tambayi AI "ta yaya BF zai samar da wani sakamako na daban a cikin shekarar da ta gabata" kuma kwatanta hanyoyin biyu. A hankali karkatar da ɗayan abubuwan (misali, faɗaɗa tantanin halitta da sau 10) kuma lura da yadda martanin AI ke canzawa da kuma yadda tantancewar tantancewa zai kama wannan.
jerin abubuwan dubawa
- [ ] Shin na yi daidai da ko na saita alwatika bisa la'akari da lalacewa da aka biya ko lalacewa?
- [ ] Shin na duba yiwuwar ta hanyar kwatanta abubuwan shekarun shekaru da tsarin tarihi?
- [ ] Shin na yi rajista tare da BF don sababbin / shekaru marasa girma?
- [ ] Na gabatar da amsa tare da kewayon rashin tabbas maimakon lamba ɗaya?
- [ ] Shin na sake ƙididdige lalacewar ƙarshe da lissafin lissafi da kansa?
- [ ] Shin na sanya hujjar zaɓi na factor (matsakaicin nau'in, lokaci) a rubuce?