Riba:
- Ƙarfin ƙididdigewa da fassara teburin mace-mace, yuwuwar rayuwa, shekara-shekara (gudanar da biyan kuɗi na yau da kullun) da gabatar da ra'ayoyin ƙima tare da tallafin fasaha na wucin gadi.
- Ability don bincika sha'awar fasaha (ƙididdigar ragi), ƙimar abin alhaki da farfadowar mace-mace / haɗarin tsawon rai akan yanayin yanayin tare da hankali na wucin gadi.
- Ƙarfin rarrabewa cewa asusun rayuwa / ritayar da aka samar ta hanyar basirar wucin gadi ya dogara ne akan zaɓin tebur, sha'awa da zato, kuma waɗannan zato sune alhakin aikin.
Inshorar rayuwa da fansho masu zaman kansu sune mafi tsufa kuma mafi yawan fannonin ilimin lissafi na kimiyyar aiki. Manufar inshorar rayuwa tana iya ɗaukar shekaru 40; Aikin fensho ya ƙunshi albashin da mutumin da ya kai shekaru 30 a yau za a biya bayan shekaru 65. Don daidai darajar irin waɗannan basussukan na dogon lokaci a yau, ana buƙatar mahimman bayanai guda biyu: ta yaya mutane za su tsira (mutuwa) da ƙimar kuɗi akan lokaci ( riba / rangwame). A cikin wannan rukunin, za mu rufe tebur ɗin mace-mace, yuwuwar rayuwa, ƙimar kuɗi da ƙimar abin alhaki a kusa da waɗannan gatura biyu; Za mu ga yadda ake amfani da AI lafiya a cikin waɗannan asusun.
Bari mu tunatar da ku tun daga farko: asusun rayuwa da na ritaya sun dogara gaba ɗaya akan zato - wane tebur mace-mace, wacce ƙimar riba, wacce yanayin dawowa. AI yana yin lissafin kuma ya rubuta lambar, amma zaɓi da alhakin waɗannan zato ya ta'allaka ne ga mai yin aiki. Taswirar da ba daidai ba ko zaɓin sha'awa ya zama kuskuren tsari wanda ya wuce shekaru da yawa.
Teburin mutuwa da rayuwa
Tushen kowane asusun rayuwa / ritaya shine tebur na mace-mace (tebur na mutuwa). Wannan tebur yana ba da yuwuwar asali ga kowane shekaru: qx, wato, yuwuwar mutumin da ya kai shekaru x zai mutu a cikin shekara guda. Misali, idan q65 = 0.012, yuwuwar mai shekaru 65 ya mutu a cikin shekara guda kusan kashi 1.2 ne. Daga wannan, ana samun yuwuwar tsira shekara guda tare da px = 1 - qx. Ta hanyar sarkar shekaru da yawa, tPx (yiwuwar wani yana da shekaru x zai rayu wata t shekaru) ana ƙididdige su: tPx = px × px+1 × ... × px+t−1.
Akwai allunan da ake amfani da su sosai a cikin fensho masu zaman kansu a cikin Turkiye (misali, abubuwan da suka samo asali na CSO da tebur na gogewa na ƙasa); kamfanoni suna daidaita waɗannan bisa ga gogewar fayil ɗin su. Mahimmin mahimmanci: zato mai hankali don inshorar rai (biya akan mutuwa) shine mafi girman mace-mace, don shekara-shekara (biya kamar yadda kuke raye) ra'ayin ra'ayin mazan jiya shine ƙananan mace-mace (tsawon rai). Tebur iri ɗaya yana wakiltar haɗari daban-daban dangane da jagorancin samfurin.
Tukwici: Kar a sanya AI ta faɗi sunan tebur na mace-mace - ƙirar na iya haɗa sunan tebur da ƙimar qx. Ɗauki tebur daga tushen hukuma, yi amfani da AI don ƙididdigewa kawai tare da waɗannan ƙimar.
Ƙimar yanzu, riba da kuɗin shiga
Axis na biyu shine ƙimar lokaci na kuɗi. 100 TL da muke da shi a yau ya fi 100 TL a shekara daga baya; saboda ana iya saka hannun jari da samar da riba. Rangwamen biyan kuɗi na gaba zuwa yau ana kiransa rangwame, kuma adadin da aka yi amfani da shi ana kiransa riba ta fasaha (ƙididdigar ragi). Ana samun darajar yanzu na 1 TL bayan shekaru t ta vᵗ = 1 / (1+i) ᵗ; inda nake sha'awar fasaha. Dangantaka mai mahimmanci: yayin da sha'awa ke ƙaruwa, ƙimar halin yanzu na biyan kuɗi na gaba yana raguwa saboda ana amfani da rangwamen da ƙarfi.
Annuity wani rafi ne na biyan kuɗi na yau da kullun (misali, fansho da ake biya kowace shekara). Ƙimar kuɗin rayuwa na yanzu ya haɗu da bayanai guda biyu: ko dole ne mutum ya kasance da rai har sai an biya kowane biya (mutuwa) da kuma yadda za a rage wannan biyan zuwa yanzu (sha'awa). A sauƙaƙe, ƙimar kuɗin da ake biyan $1 a kowace shekara don rayuwa ga wani mai shekaru x shine:
äx = Σ (tPx × vᵗ) - wato, jimlar "yiwuwar rayuwa zuwa waccan shekarar × rangwamen rangwame" na kowace shekara mai zuwa.
Wannan dabara guda ɗaya ita ce ginshiƙi na ƙididdige ƙimar inshorar rai da alhaki na ritaya. AI cikin sauri ya ɓoye wannan jimlar; amma tebur da zato na sha'awa waɗanda ke ciyar da tPx da vᵗ naku ne.
Teburin mai zuwa yana taƙaita mahimman ra'ayoyi:
ra'ayi
alama
Ma'ana
yiwuwar mutuwa
qx ku
Yiwuwar mutuwa a cikin shekara da shekaru x
tsira
px = 1-qx
Yiwuwar yin rayuwa shekara ɗaya da shekaru x
t shekara tsira
tPx
mai shekara x yana rayuwa don t fiye da shekaru
rangwamen kudi
vᵗ = 1/(1+i) ᵗ
Ƙimar yanzu na 1 TL bayan shekaru t
kudin rayuwa
ku
Ƙimar yanzu na biyan 1 TL kowace shekara don rayuwa
Alhaki, farfadowar mace-mace da haɗarin rayuwa mai tsawo
Alhaki na fensho ko kamfanin rai shine darajar yanzu na duk kuɗin da aka samu da diyya da zai biya a nan gaba. Wannan ƙimar tana da matuƙar kula da zato guda uku: teburin mace-mace, sha'awar fasaha, da zato na kashewa/ sokewa. Babban haɗari mai haɗari shine haɗarin rayuwa mai tsawo: idan mutane sun rayu fiye da yadda ake tsammani, biyan kuɗin shekara ya zama tsayi kuma abin alhaki yana ƙaruwa. Don haka a maimakon tebur na tsaye, masu yin aiki suna amfani da haɓakar mace-mace: hasashen da ke ɗaukan yiwuwar mutuwa zai ragu kaɗan kowace shekara. AI na iya ƙididdigewa da sauri da kwatanta tasirin abin alhaki na yanayin dawowa daban-daban.
Tsanaki: Ƙananan canji a cikin sha'awa ko mace-mace yana yin babban tasiri akan abin alhaki na dogon lokaci. Rage sha'awar fasaha da kashi 0.5 na iya ƙara wajabcin shekara 30 ta hanyar adadin lambobi biyu. Saboda haka, zato suna barata ɗaya bayan ɗaya kuma ana yin nazarin hankali.
Yadda ake amfani da AI a cikin lissafin rayuwa / ritaya
1) Rayuwa da lambar asusun ajiyar kuɗi:
Rubuta lambar tare da sharhi a cikin Python:Input: shekarun qx dabi'u daga 60 zuwa 100 (jerin da zan bayar), sha'awar fasaha i=0.04.1) Ƙirƙirar tPx (tsira da rayuwa daga 60) ga kowane shekaru.2 * v^t) Yi lissafi. Buga matsakaicin ƙima. KAR KA KARYA qx's; Zan ba shi.
2) Hankalin sha'awa:
Na ƙididdige ƙimar shekara ta yanzu don i=0.04: 14.8. Sake ƙididdige ƙimar yanzu don i=0.03, 0.05, 0.06 tare da tPx iri ɗaya. Yi tebur na sakamakon kuma bayyana a cikin jumla ɗaya dalilin da yasa ƙimar ke raguwa yayin da sha'awa ke ƙaruwa.
3) Halin tsawon rai:
Matsayinku: mataimakiyar actuary life. Abin alhaki na shekara-shekara a shekara 65 tare da mace-mace a tsaye shine raka'a 12.4. Ta yaya zan aiwatar da yanayin 'farfadowar mace-mace' inda qxs ke raguwa da 1% kowace shekara? Bayyana manufar, jera matakan lissafi. Ana sa ran alhakin ya karu ko raguwa, me yasa?
4) Fassara sakamakon zuwa gudanarwa:
Lokacin da na rage yawan riba na fasaha daga 4% zuwa 3.5%, alhakin ritaya na ya karu da kashi 11%. Bayyana wannan ga kwamitin gudanarwa a cikin jimloli 4: - Me yasa abin alhaki ya karu lokacin da adadin riba ya ragu? - Shin wannan fitowar tsabar kuɗi na gaske ne ko tasirin ƙima? - Rubuta kasada 2 da yakamata gudanarwa ya kula.
Rauni mai ƙarfi / Ƙarfi mai ƙarfi
Rawanin faɗakarwa:
Yi ƙididdige ƙimar fensho na yanzu ga mai shekara 65.
Ba a bayar da tebur na mace-mace, ko riba, ko adadin biyan kuɗi ba. AI ya dace da tebur da qx; sakamakon ba shi da ma'ana.
Ƙarfi mai ƙarfi:
Matsayin ku: mataimakin kididdigar lissafin kuɗi zuwa pension actuary.Input (Na bayar): 65-90 shekaru qx dabi'u: [jerin a nan] - Fa'idar fasaha i = 0.04- Annuity: 1 unit, a farkon shekara, don lifeTask: 1) Yi lissafta tPx da v^t.2) Nemo darajar yanzu tare da täxΣ 3 annuity). matsakaicin matakan da hannu don haka zan iya tabbatarwa.qx da sha'awa KADA KA YI KARYA; Kawai amfani da abin da na ba ku. Idan ya ɓace, tambaya.
uku mini lokuta
Case 1 - Ƙarfin tunanin sha'awa. Kamfanin fensho ya ƙididdige alhakinsa a matsayin TL miliyan 480 tare da kashi 5 cikin ɗari na sha'awar fasaha. Lokacin da farashin ribar kasuwa ya ragu, mai gudanarwa ya so a yi amfani da kashi 3.5 cikin ɗari. An sake ƙididdige shi akan tushen mace-mace iri ɗaya kamar AI: alhaki ya karu zuwa miliyan 560, karuwar kashi 17 cikin ɗari. Kamfanin yana buƙatar ware ƙarin jari. Darasi: Sha'awa kadai yana da babban tasiri akan abin alhaki na dogon lokaci.
Case 2 - Mamakin Tsawon Rayuwa. Fayil ɗin ya yi farashin shekara-shekara tare da tsayayyen tebur na mace-mace shekaru 20 da suka gabata. Mutanen da ke da inshora sun rayu matsakaicin shekaru 3.5 fiye da yadda ake tsammani; An tsawaita biyan kuɗi kuma fayil ɗin ya jawo asara. An ƙara haɓaka mace-mace a farashi na gaba. AI ta ƙididdige bambanci tsakanin ainihin mutuwar tarihin tarihi da tebur (A / E rabo - ainihin / tsammanin) kuma ya nuna buƙatar ingantawa; Mai wasan kwaikwayo ya yanke shawara.
Case na 3 - Tarkon tebur da aka yi. Wani mataimaki ya tambayi YZ, "Mene ne ƙimar q70 na ginshiƙi na TRH-2010?" "0.0185," in ji AI da tabbaci. Mataimakin ya sanya shi a cikin asusun. A cikin ainihin tebur, ƙimar ta bambanta kuma sunan tebur bai yi daidai ba. Da zarar an tabbatar, an bayyana bambancin kuma an gyara duk asusun. Darasi: qx da sunayen tebur ba a taɓa dawowa daga ƙwaƙwalwar AI ba; An shigar da shi daga majiyar hukuma.
Kuskuren gama gari
- Yin AI ya dace da teburin mace-mace ko qx's. Wadannan sun fito ne daga majiyar hukuma; AI yakamata yayi lissafin kawai tare da ƙimar da kuke bayarwa.
- Yin la'akari da tasirin sha'awar zato. Ƙananan canjin kuɗin ruwa yana haifar da babban bambanci a cikin abin alhaki na dogon lokaci; Ana buƙatar nazarin hankali.
- Yin amfani da mace-mace a tsaye da yin watsi da haɗarin dadewa. Idan ba a haɗa murmurewa ba, ana ƙididdige alhaki na shekara-shekara bisa tsari.
- Hanyar samfur mai ruɗani. A cikin inshorar rayuwa, yin taka tsantsan shine don yawan mace-mace da yawan kuɗi don ƙarancin mace-mace; Tebur iri ɗaya yana nufin haɗari daban-daban.
- Rikita tasirin kimantawa tare da fitar da tsabar kudi. Ƙarar abin alhaki na tushen riba ba biyan kuɗi ba ne nan da nan, amma auna ƙimar yanzu.
A takaice
Asusun rayuwa da na ritaya sun dogara ne akan gatari biyu: mace-mace (tsira da qx, px, tPx) da riba (ragi tare da vᵗ). Waɗannan suna haɗuwa don ba da ƙimar halin yanzu na shekara-shekara da alhaki (äx = Σ tPx·vᵗ). Yayin da sha'awa ke ƙaruwa, ƙimar yanzu tana raguwa; Hadarin dadewa yana haifar da alhaki kuma ana sarrafa shi ta hanyar dawo da mace-mace. AI yana ƙididdige waɗannan jimlar cikin sauri kuma yana kwatanta yanayin; Amma zabi da alhakin teburin mace-mace, sha'awa da zato na farfadowa yana tare da mai aiki. Makullin ba shine yin zato ya dace da AI ba, amma don ciyar da shi daga tushen hukuma kuma ya sa AI ta yi lissafin.
Aikin aikace-aikace
Fito da ɗan gajeren jerin qx's (misali shekaru 65-80, daga tebur na yau da kullun ko misalin lacca) da sha'awar fasaha. Tambayi AI don ƙididdige (a) tPx da vᵗ, (b) ƙimar kuɗin rayuwa na yanzu. Da hannu tabbatar da ƙimar tPx da vᵗ don shekaru 3 na farko. Sa'an nan kuma lura da yadda darajar yanzu ta canza ta karuwa/rage yawan riba da maki 1 kuma lura da tasirin kashi.
jerin abubuwan dubawa
- [ ] Shin na ɗauki teburin mace-mace da qx's daga tushen hukuma ko ban sami daidaita su ta hanyar AI ba?
- [ ] Shin na ba da hujjar zato na sha'awa na fasaha kuma na gudanar da bincike na hankali?
- [ ] Shin na yi la'akari ko ana buƙatar dawo da mace-mace don haɗarin dadewa?
- [ ] Shin da hannu na tabbatar da ƴan tPx na farko da ƙimar vᵗ?
- [ ] Shin na zaɓi hanyar ajiyar da ta dace da jagorar samfurin (rayuwa vs annuity)?
- [ ] Shin na gabatar da canjin abin alhaki daidai ba tare da ruɗe shi da fitar da kuɗi ba?