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*anoue 1. I?iaeaia iao/aiey.

Aaaaeaiea

Iauea iieiaeaiey.

Aeaiiay i?iaeaia caeeth/aaony a auai?a iaaeaeo o/aaie e ?aaioie. Ia?aae
oaeei auai?ii noaiiaeony eaaeaeue /aeiaae, ieii/eaoee 11-ue eeann,
eiaaea o /aeiaaea anoue 2 aeueoa?iaoeau: i?iaeieaeaoue o/eoueny aeaeueoa
eee n?aco ia/aoue ?aaioaoue, ieii/ea eo?nu ii aoaeouae niaoeeaeueiinoe.
Aeaiiay i?iaeaia aieaa aeooaeueia aeey auioneieoe, /ai aeey auioneieeia,
oae eae ia?ie iinooiatho a aunoea o/aaiua caaaaeaiey ia oieueei n
oeaeueth iao/aiey, ii e aeey ion?i/ee i?ecuaa a a?ieth.

Aaoi?u aeaiiie ?aaiou oiaea noiyee ia?aae aeaiiui auai?ii. Ai a?aiy
auai?a, e niaeaeaieth, iunee i ?aoaiee aeaiiie i?iaeaiu ia ieii/aoaeueii
noi?ie?iaaeenue, e iiyoiio aaoi?ai i?eoeinue ?oeiaiaenoaiaaoueny ia
noieueei iaoaiaoe/aneeie ?an/aoaie, neieueei i?aae/oanoaeai, niaaoii
iiae?oa e ?iaeeoaeae, a oaeaea eo ee/iui i?eia?ii.

Aeueoa?iaoeaa 1 – ia/eiaoue ?aaioaoue n?aco iinea ieii/aiey oeieu

Oeieueiia ia?aciaaiea e ona?aeiia naiiiao/aiea auioneieea oeieu aeaeaao
aai i?eaiaeiui e aieueoiio niaeo?o ?aaio, ia o?aaothueo niaoeeaeueiiai
aunoaai ia?aciaaiey, iniaaiii a i?aaiecaoeee, aaea ?aaioatho
?iaenoaaiieee e aeeceea ae?ocuey auioneieea e ?iaeeoaeae. I?e yoii
nouanoaoao aiciiaeiinoue iinooieaiey ia ioiineoaeueii iaaunieoth
aeieaeiinoue.

Aeinoieinoaa aeaiiie aeueoa?iaoeau:

aeecinoue e i?aeoe/aneei, ?aaeueiui i?iaeaiai iicaieytho /aeiaaeo
iao/aoueny iaeiia?aiaiii n ?aaioie, ia o?aoy a?aiaie ia niaa?oaiii
aaniieaciua i?aaeiaou aunoaai ia?aciaaiey, oaeeo eae oeeinioey,
eoeueoo?ieiaey, oeiey e oiio iiaeiaiua.

niaao eieeaa e ciaeiiuo iiaoo oaeaea nua?aoue aieueooth ?ieue a oceii
i?ioanneiiaeueiii ia?aciaaiee.

anee ?a/ue eaeao i aooaaeoa?neeo niaoeeaeueiinoyo, i eioi?uo i?aaeaea
anaai aeoiaea iaeia ec aaoi?ia, oi nouanoaoao ia?iiiia eiee/anoai
eeoa?aoo?u, iinayuaiiia aeaiiiio i?aaeiaoo. Oaeaea oe?iei ?ani?ino?aiaiu
eo?nu ii iiaeaioiaea ii ?acee/iui niaoeeaeueiinoyi, aeeth/ay iaiaaeaea?a
e aooaaeoa?a. Eae i?aaeei, aunoaa ia?aciaaiea ii aeaiiui
niaoeeaeueiinoyi ieaoiia, e noieiinoue iao/aiey a AOCao ii aeaiiui
niaoeeaeueiinoyi ai?acaei aei?iaea noieiinoe iao/aiey ia anaaiciiaeiuo
eo?nao. E oiio aea, i?aaiecaoeee, aaaeoueo eo?nu ii iiaeaioiaea e
aeaiiui i?ioanneyi, aeinoaoi/ii iiiai, /oi iaeuecy neacaoue i?i AOCu.
I?e iaeeee i?aaiecaoeee iiaeii iiaeia?aoue eo?nu, ia io?uaathuea
/aeiaaea io ?aaiou.

/oi /aeiaae, ono?ieaoenue ia ?aaioo, eiaao aiciiaeiinoue ia i?aeoeea
ioneaaeeaaoue neooaoeeth a eiie?aoiie i?ioanneiiaeueiie iaeanoe –
iai?eia?, eaeea niaoeeaeenou o?aaothony e n eaeeie ciaieyie.

/aeiaae eiaao aiciiaeiinoue iiaeno?aeaaoue i?ioeann (naii)iao/aiey iiae
naay, aua?aoue naaa ioaa/athuea aai o?iaith ciaiee eo?nu, aeinoaaaoue
eeoa?aoo?o ia o?aaoaiii o?iaia ciaiee. Anoanoaaiii, yoa iniaaiiinoue
iiaeao i?iyaeoueny oieueei i?e iaee/ee ioiineoaeueii aunieie eoeueoo?u
naiiia?aciaaiey, iaee/ey neeu aiee o /aeiaaea, iiiiue ci noi?iiu
ie?oaeathueo.

Iaaeinoaoee aeaiiie aeueoa?iaoeau.

E iaaeinoaoeai oaeiai iooe iiaeii ioianoe oi, /oi aeiaieueii o?oaeii
iieo/eoue aunieieeanniia ia?aciaaiea ia eo?nao iiaeaioiaee ii
niaoeeaeueiinoyi eee naiinoiyoaeueii.

iao/aiea naiinoiyoaeueii oiaea o?aaoao iaeioi?ua n?aaenoaa ia o/aaioth
eeoa?aoo?o.

ionoonoaea aeeieiia i iieo/aiee aunoaai ia?aciaaiey, eioi?ue eiaao
ai?acaei aieueoee aan, /ai aeeieiiu anaaiciiaeiuo iiaeaioiaeoaeueiuo
eo?nia. Ii aeaiiue iaaeinoaoie eiaao iaeii “ii”. Iaee/ea aeeieiia
o?aaoaony (eee aeaeaoaeueii) i?e i?eaia ia ?aaioo. Anee /aeiaae
ono?ieony n?aco, oi ono?aeaaoueny aio aieueoa ia i?eaeaony ( a eaeaaea).
A ooaeoai neo/aa oio aea aeeieii iiaeii eoieoue n ethauie o?aaoaiuie
ioeaieaie. Aua iaeiei ec aeinoieinoa ?aaiou iinea ieii/aiey oeieu
yaeyaony oi, Oaeaea e aeinoieinoaai ioiineony oi, /oi

iaeue eiioaeo ni naa?noieeaie. A eieeaeoeaa, aaea aoaeao ?aaioaoue
/aeiaae, nei?aa anaai aoaeoo ?aaioaoue aieaa noa?oea ethaee. Cia/eiinoue
aeaiiiai oaeoi?a oeaeeeii caaeneo io ee/iinoiuo iniaaiiinoae /aeiaaea.

Aeueoa?iaoeaa 2 – nia/aea ieii/eoue AOC, a iioii ia/eiaoue ?aaioaoue.

Ae?oaie aeueoa?iaoeaie yaeyaony iao/aiea a AOCa ii aua?aiiie
niaoeeaeueiinoe. A aieueoeinoaa neo/aaa iao/aiea a AOCa ieaoiia.

Aeinoieinoaa aeaiiiai iooe:

oaeoaeaiiia ia?aciaaiea a eiie?aoiie iaeanoe e oe?ieee i?ioanneiiaeueiue
e?oaici? a oeaeii niaeo?a iaeanoae.

iieo/aiea aeeieiia. I?anoeaeiinoue aeeieiia caaeneo io i?anoeaeiinoe
AOCa.

o/eoaey a i?anoeaeiii AOCa eae i?aaeei eiatho aieaa aunieoth
eaaeeoeeaoeeth, /ai i?aiiaeathuea eo?nu iiaeaioiaee ii i?ioanneyi.

Iaaeinoaoee aeaiiiai iooe:

ionoonoaea aiciiaeiinoe ?aaeeciaaoue naay a iieiie ia?a. Anee nooaeaiou
a?oiiu, a eioi?ie o/eony /aeiaae, iaeaaeatho ieceie iiaeaioiaeie e
i?ioanneiiaeueiuie ciaieyie, oi a iiaeaaeythuai aieueoeinoaa AOCia
iaaeaaiae aoaeoo i?eaioe?iaaiu eiaiii ia yoi iaeiciathuaa aieueoeinoai.

ionoonoaea aiciiaeiinoe ei??aeoe?iaaoue i?ioeann iieo/aiey ciaiee e
ia?aoiay naycue n i?aaeiaoiie iaeanoueth. Oaeei ia?acii, anee /aeiaae
ociaao, /oi ni?in ia i?ioanneth, eioi?oth ii iieo/eo, ?acei oiae, oi aio
i?eaeaony auno?i ia?ao/eaaoueny ia ae?oaoth i?ioanneth.

aieaa aunieay ieaoa ca iao/aiea, /ai ia niaoeeaeece?iaaiiuo eo?nao.

io iiiaioa iieo/aiey ciaiee aei eo aeoeaiiai i?eiaiaiey i?ioiaeeo
aeiaieueii cia/eoaeueiia a?aiy.

iaaiciiaeiinoue ?aaioaoue ia?aeeaeueii n o/aaie a AOCa.

noaiaea?o ia ainoaea?noaaiiia ia?aciaaiea auioaeaeaao iao/aoueny
anaaiciiaeiui iaioaeiui i?aaeiaoai. Anee /aeiaae iieiinoueth inaiee
aeaiiue i?aaeiao naiinoiyoaeueii aua aei aai i?aiiaeaaaiey, oi ii iiaeao
naeaoue yecaiai yenoa?iii ii aeaiiiio i?aaeiaoo. A yoii neo/aa ieaoa ca
iao/aiea ia eciaieony, oi anoue aeaiueae ca naeaiiue yenoa?iii eo?n ia
aoaeoo aica?auaiu. E oiio aea ia ana i?aiiaeaaaoaee iaeia?ytho
aein?i/ioth naea/o yecaiaia eee ia?aca/ao, oi anoue nouanoaoao
aa?iyoiinoue, /oi caiyoey ii aeaiiiio i?aaeiaoo ana-oaee i?eaeaony
iinauaoue.

Oaeei ia?acii, a iaeioi?uo neo/ayo iiaeao ieacaoueny i?aaeii/oeoaeueiaa
ia o/eoueny a AOCa, a n?aco ia/eiaoue ?aaioo, anee oaeiaay anoue, e,
aiciiaeii, naiiia?aciaaiea.

Aeaiiay ?aaioa i?aaeeaaaao iaoiae ioeaiee e auai?a iaeiiai ec aeaoo
auoaoeacaiiuo aa?eaioia.

Iaoiae ioeaiee aeueoa?iaoea.

Iauea iieiaeaiey.

Iaoiae ioeaiee iniiaai ia au/eneaiee ca?aaioiie ieaou, eioi?oth /aeiaae
iiaeao iieo/eoue, iieaey ii iaeiiio ec aeaoo iooae, ioe?uaathueony iinea
ieii/aiey oeieu. Oaeei ia?acii, iu au?aaeaai i?aaeii/oeoaeueiinoue
eaeiai-eeai iooe /a?ac noiia?ioth ca?aaioioth ieaoo, eioi?oth /aeiaae
iieo/eo ca N eao. Iaoiae ia o/eouaaao ii?aeueii-ineoieiae/aneie
cia/eiinoe eaeiai-eeai iooe, iai?eia?, iiuo, iieo/aiiue io iauaiey ni
naa?noieeaie a einoeoooa. Oae aea ia o/eouaathony anaaiciiaeiua
neo/aeiua niauoey, oaeea eae nia?oue ?iaenoaaiieea, auoiae caioae eee
?iaeaeaiea ?aaaiea e oiio iiaeiaiia. Aeey iauaeoeaiinoe ioeaiee
iaoa?eaeueiie noi?iiu aii?ina ana aeaiaaeiua aaee/eiu aa?oony ia iiiaio
t0 – a?aiy i?eiyoey ?aoaiey, oaeei ia?acii o/ao eioeyoeee aeieaeai auoue
naeaeai i?e caaeaiee enoiaeiuo aeaiiuo.

Iaoaiaoe/aneay iiaeaeue i?iaeaiu.

Aeaiiay iaoaiaoe/aneay iiaeaeue i?iaeaiu eniieuecoao niaoeeaeueii
?ac?aaioaiioth aeey aeaiiie ?aaiou iiaeaeue ea?uea?u /aeiaaea, a
/anoiinoe ca?ieaou /aeiaaea a ioee/ee io a?aiaie.

Iiaeaeue ea?uea?u /aeiaaea.

Aoaeai n/eoaoue, /oi n oa/aieai a?aiaie t /aeiaae aoaeao iieo/aoue
ca?ieaoo, ?aaioth

W = at^2 + bt + c (1)

au?aaeaiea (1) yaeyaony o?aaiaieai ia?aaieu. A iai a, b – eiyooeoeeaiou,
ii?aaeaeythuea nei?inoue ?inoa ea?uea?u.

n – ieieiaeueiay ca?ieaoa, iia ?aaia ca?ieaoa, eioi?oth iieo/eo /aeiaae
a iiiaio o?oaeiono?ienoaa.

Eiyooeoeeaiou a e b – ioaa/atho ca nei?inoue ?inoa ca?ieaou /aeiaaea,
iaoneiaeaiiua eae iiauoaieai noaaea, oae e ia?aoiaeii ia iiaua (aieaa
aunieea) aeieaeiinoe. A ethaie i?aaiecaoeee a,b>=0. I?e aieueoeo
cia/aieyo a aiai?yo i aa?oeeaeueiie ea?uea?a, a i?e a=0 e b<>0 aiai?yo i
iiiioiiiii i?ioanneiiaeueiii ?inoa. Ca?ieaoa, eioi?oth /aeiaae iieo/eo a
/enoii aeaea ca ia?eiae (t=0;t=T), aoaeao au?aaeaoueny eioaa?aeii

= aT^3/3 + bT^2/2 + cT (2)

*oi /aeiaae iiaeao naeaeaoue n yoeie aeaiueaaie? Nouanoaoao aeaa
aa?eaioa. Ia?aue – ii n?aco eo o?aoeo oeaeeeii. Aoi?ie – ii /anoue
o?aoeo, /anoue ioaeaao a aaie iiae i?ioeaio p. Aoaeai n/eoaoue, /oi
/aeiaae aeaenoaoao ii aoi?iio aa?eaioo e ii o?aoeo aeaiueae oiaea ii
eaaae?aoe/iiio caeiio, oi anoue aai cao?aou a iiiaio a?aiaie t
ninoaaeytho

E= dt^2 + dt + f (2)

Iniiaiui oneiaeai nouanoaiaaiey /aeiaaea yaeyaony

a>= d, b>=d, c>=f (3)

I?e iaauiieiaiee yoiai oneiaey /aeiaae inoaaony aac aeaiaa. Aoaeai
n/eoaoue, /oi cao?aou /aeiaaea n aeinoaoi/iie noaiaiueth oi/iinoe
iienuaathony oi?ioeie (2).

Iinea ii?aaeaeaiiuo ?anoiaeia o /aeiaaea inoaaony aeaiaa

L = S – E. (4)

Yoe aeaiueae ii iaoae iiaeaee /aeiaae ioaeaao iiae i?ioeaio p,
ian/eouaaaiue ca eaaeaeue eioa?aae a?aiaie. Iu n/eoaai, /oi i?ioeaio
ia/eneyaony eaaeaeue aiae ii aaiiao?e/aneie i?ia?annee. Iu
i?aaeiieaaaai, /oi /aeiaae eaaeaeue ianyoe caaiaeeo n/ao ia inoaoee io
ca?ieaou, caaiaey eaaeaeue ianyoe iiaue n/ao e /oi caaaaeaiea iiaiai
n/aoa aaniethoii aanieaoii. N?aaenoaa, eioi?ua /aeiaae nieiao /a?ac K
ia?eiaeia aoaeoo au?aaeaoueny ii oi?ioea:

Y= (L(1+p/100))^K. (5)

Aoaeai n/eoaoue, /oi i?e iaoeaeii K noiia aeinoaoi/ii aeecei
ai?ieneie?oaony au?aaeaieai (5). Aiiaua, ii?yaeie auieaou caaeneo io
oneiaee eiio?aeoa n aaieii.

O eaaeaeie aeueoa?iaoeau nouanoaoao aeaa aa?eaioa oeiaine?iaaiey a
oa/aiea a?aiaie, eiaaea /aeiaae ia ?aaioaao. A ia?aii neo/aa /aeiaae
ao?ao n?aaenoaa o ?iaenoaaiieeia a e?aaeeo aac i?ioeaioia, a ai aoi?ii
aeaiueae ia iao/aiea e i?iaeeaaiea aei iieo/aiey ia?aie ca?ieaou aa?oony
eaaeaeue ianyoe a e?aaeeo iiae i?ioeaiou ( iiaeao auoue aeaaea e o oao
aea ?iaenoaaiieeia). Ii yoie i?e/eia i?e ioeaiea eaaeaeie aeueoa?iaoeau
?anniao?eaaaony aeaa aa?eaioa: eiaaea i?ioeaioa e?aaeeoa =0 e eiaaea ii
ia?aaai.

Eniieuecoy i?eaaaeaiioth auoa iiaeaeue, iu iiaeai au/eneeoue noiio,
eioi?oth /aeiaae iiaeao iieo/eoue ca N ianyoeaa, ia/aa n?aco ?aaioaoue
eee ia/aa ?aaioaoue iinea iao/aiey a AOCa. N/eoaai, /oi /aeiaae ia/eiaao
i?eieiaoue ?aoaiea a iiiaio a?aiaie t=0.

III. Iaoiaeeea ?an/aoa i?e aani?ioeaioiii e?aaeeoa.

Aa?eaio – n?aco ?aaioaoue

Aoiaeiua aeaiiua:

a1, b1, c1 – ia?aiao?u ?aaiou, ia eioi?oth /aeiaae ono?aeaaaony.

d1, e1, f1 – ia?aiao?u ?anoiaeia /aeiaaea.

t01 – a?aiy ono?ienoaa ia ?aaioo. Anee t01<>0, n/eoaai, /oi aei ia/aea
?aaiou /aeiaae iio?aaeyao ii caeiio E=f01 ( oi anoue iaeio e oo aea
noiio), iaoiaeynue ia eaeaeeaaiee o ?iaenoaaiieeia. Noiio iioii ii
ioaeaao aac o/aoa noaaee i?ioeaioa (ana-oaee yoi ?iaenoaaiieee). N/eoaai
t01 – iiia? ianyoea, n eioi?iai /aeiaae ca/eneai ia ?aaioo.

Oaeaea n/eoaai, /oi /aeiaae o?aoeo ia eo?nu ii iao/aieth. Ionoue ii
cao?a/eaaao ia eo?nu a noiia Q1 aeaiaa aei ia/aea iieo/aiey ca?ieaou.

N/eoaai, /oi ii i?ioiaeeo eo eeai ia naie, eeai ia aeaiueae
?iaenoaaiieeia, n oneiaeai iineaaeothuaai aica?auaiey. A ethaii neo/aa,
aeaiueae ca eo?nu ii ioaeaao (“auueiuaaao”) ec nianoaaiiuo ?anoiaeia, oi
anoue aai ?anoiaeu iinoiyiii iiae/eiythony (2), iacaaeneii io oiai,
eaeay /anoue ec ieo caiea/aia ca eo?nu, a eaeay – iio?a/aia ia ee/iua
ioaeaeu.

Noiia aeaiaa E1, eioi?oth /aeiaae ioaeano ?iaenoaaiieeai, aoaeao
au?aaeaoueny eae

E1=f01*(t01+1) + Q1

Oiaaea ca?ieaoa, eioi?oth ii iieo/eo ca N ianyoeaa, aoaeao au?aaeaoueny
aaee/eiie I1

I1= (a1-d1)/3(N-t01)^3 + (b1-e1)/2(N-t01)^2 + (c1-f1)(N-t01)

Eoiaiaoth noiio aeaiaa M1, eioi?ie /aeiaae aoaeao iaeaaeaoue /a?ac N
ianyoeaa, aoaeao au?aaeaaony oi?ioeie

M1 = I1- E1 (6)

Aeaiiay oi?ioea ni?aaaaeeeaa i?e ethaii t>=t01. (I?e yoii aeaiueae,
caiea/aiiua ca eo?nu, iu n?aco o/eouaaai). Aeaiiay oi?ioea iieacuaaao,
neieueei aeaiaa aoaeao eiaoue nai /aeiaae i?e aeaaineeiiiinoe naieo
?iaenoaaiieeia. A iae iu ia o/eouaaai, /oi ?iaenoaaiieee iiaee
iieiaeeoue cao?a/aiiua aeaiueae a aaie iiae oio aea i?ioeaio p –
naiaia?aciue yaienoe/aneee iiaeoiae.

Aa?eaio – o/eoueny, iioii ?aaioaoue

Aoiaeiua aeaiiua

a2, b2, c2 – ia?aiao?u ?aaiou, ia eioi?oth /aeiaae ono?aeaaaony.

d2, e2, f2 – ia?aiao?u ?anoiaeia /aeiaaea.

t02 eiee/anoai ianyoeaa, /a?ac eioi?ia /aeiaae ono?ieeny ia ?aaioo iinea
ieii/aiey AOCa. Aeaiiay aaee/eia iiaeao eiaoue io?eoeaoaeueiia cia/aiea
( /aeiaae ia/ae ?aaioaoue, aa iao/aynue a einoeoooa).

t12 – eiee/anoai ianyoeaa, /a?ac eioi?ia /aeiaae ia/eiaao o/eoueny
(ia/aei naiano?a).

?anoiaeu ia aeiiieieoaeueiua eo?nu, iao/aiea caaeathony a aeaea
iiiaeanoaa S2i, aaea i-aaniethoiue iiia? ianyoea, a eioi?ue i?iecaaaeai
i-ue ?anoiae. Oaeaea caaeaaony ianyoe te2, a eioi?ue /aeiaae caeai/eaaao
aeaeaoue ?anoiaeu ia eo?nu e ia?aciaaiea, ia aeeth/ay ieaou ca AOC.
Oaeaea caaeaaony iinoiyiiay aaee/eia f02, eiathuay aiaeiaey n f01-
iinoiyiiuie cao?aoaie, eiaeaueieny ia iea/e ?iaenoaaiieeia. Ni.
eiiiaioa?ee e f01.

Caaeaia i?iaeieaeeoaeueiinoue o/aau a aaeeieoeao eioa?aaeao, ca eaaeaeue
ec eioi?uo o?aaoaony caieaoeoue a eiioea eioa?aaea. Eoae, U – eiee/anoai
eioa?aaeia, l – aeeeia eioa?aaea a ianyoeao, W – iieaoa, i?iecaiaeeiay a
eiioea eaaeaeiai eioa?aaea.

Iiaoi?ei eiioeaioeee aeaiiie iiaeaee: ?iaenoaaiieee aeatho aeaiueae ia
o/aao a e?aaeeo aac i?ioeaioa, n iaia?aie/aiiui n?ieii aica?aoa. I?e
aeaiiii oneiaee ieaoa ca ana ianyoeu, eioi?ua /aeiaae ia ?aaioaao,
aoaeao au?aaeaoueny neaaeothuei ia?acii:

S2i + W*U

Ia?aue /eai aeaiiie noii – iinoiyiiua ?anoiaeu. Aoi?ie – ?anoiaeu ia
eo?nu e aeiiieieoaeueiia iao/aiea. O?aoee – iieaoa ca iao/aiea a AOCa.

Oiaaea ca?ieaoa I2, eioi?oth ii iieo/eo ca N ianyoeaa, aoaeao
au?aaeaoueny aaee/eiie

I2= (a2-d2)/3(N-t12-t012-1)^3 + (b2-e2)/2(N-t12-t02-1)^2 +
(c2-f2)(N-t12-t02-1)

Eoiaiaoth noiio aeaiaa M2, eioi?ie /aeiaae aoaeao iaeaaeaoue /a?ac N
ianyoeaa, aoaeao au?aaeaaony oi?ioeie

M2=I2-E2

IV. Iaoiaeeea ?an/aoa i?e e?aaeeoiaaiee iiae i?ioeaio.

Aa?eaio – n?aco ?aaioaoue

Aoiaeiua aeaiiua:

a1, b1, c1 – ia?aiao?u ?aaiou, ia eioi?oth /aeiaae ono?aeaaaony.

d1, e1, f1 – ia?aiao?u ?anoiaeia /aeiaaea.

t01 – a?aiy ono?ienoaa ia ?aaioo. Anee t01<>0, n/eoaai, /oi aei ia/aea
?aaiou /aeiaae iio?aaeyao ii caeiio E=f01 ( oi anoue iaeio e oo aea
noiio), iaoiaeynue ia eaeaeeaaiee o ?iaenoaaiieeia. Noiio iioii ii
ioaeaao aac o/aoa noaaee i?ioeaioa (ana-oaee yoi ?iaenoaaiieee). N/eoaai
t01 – iiia? ianyoea, n eioi?iai /aeiaae ca/eneai ia ?aaioo.

Oaeaea n/eoaai, /oi /aeiaae o?aoeo ia eo?nu ii iao/aieth. Ionoue ii
cao?a/eaaao ia eo?nu a noiia Q1 aeaiaa aei ia/aea iieo/aiey ca?ieaou.

Aeey oiaiueoaiey eiee/anoaa ?an/aoia aeiaaaei e eaaeaeiio yeaiaioo
iiiaeanoaa S, eiaeaen eioi?iai iaiueoa t01, aeiaaaei aaee/eio iinoiyiiuo
?anoiaeia f01. Ia aeaiiia iiiaeanoai (S) aoaeai i?iaeieaeaoue nnueaoueny
eae ia iiiaeanoai aaee/ei ?anoiaeia ia eo?nu.

Aeey oiai, /oiau iaeoe enoeiioth noiio aeaiaa, iio?a/aiioth ia eo?nu,
i?eaaaeai niia?aaeaiey ii iiaeaee ?anieaou /aeiaaea n ?iaenoaaiieeaie.

Iaicia/ei iineaaeiee ianyoe, a eioi?ue /aeiaae i?ioiaeee iao/aiea ia
eo?nao ca te1.

Aoaeai n/eoaoue, /oi ia/eiay n ia?aie iieo/ee /aeiaae ?aniea/eaaaony n
?iaenoaaiieeaie, ioaeaaay aio noiio, eioi?oth iie au iieo/eee, iieiaeea
eiaaea-oi ioaeaiiua aio aeaiueae a aaie iiae i?ioeaio p1′. I?e yoii
aeaenoaotho neaaeothuea i?aaeea:

Eaaeaeiio ianyoeo i aei ianyoea te1 niioaaonoaoao noiia ?anoiaeia
/aeiaaea ia eo?nu Si ( a iauai neo/aa yoi ?anoiaeu, eioi?ua iai?aaeaiu
ia iao/aiea, a oii /enea e ia iieoieo eeoa?aoo?u). I?e iieo/aiee
ca?ieaou /aeiaae iuoaaony ioaeaoue aeaiueae ca iaeaieaa aeaaiee n?ie.
I?e yoii n/eoaaony, /oi ii iiaeao iio?aoeoue ana ec naieo
caieaie?iaaiiuo ?anoiaeia, e?iia v1 aeaiaa. Anee iieo/aiiay noiia
aieueoa aai ca?ieaou ieion “iaiaoiaeeiue i?iaeeoi/iue ieieioi”, oi ii
auiea/eaaao noiio ca aeaiiue ianyoe. Aeaeaa, anee inoaoee iiyoue aieueoa
v1, oi /aeiaae iiea/eaaao ca neaaeothuee ianyoe, e oae aeaeaa. Noiia?iia
eiee/anoai aeaiaa, eioi?ia ii caieaoeo, aoaeao iaoiaeeoueny neaaeothuei
aeai?eoiii:

Aeai?eoi iaoiaeaeaiey noiiu, caiea/aiiie ii e?aaeeoai

Aa?ai ia?aiaiioth t=t01+1. yoi aoaeao ia/aeueiue iiiaio a?aiaie.

Ia?aiaiioth ic=0. Aeaiiay ia?aiaiiay aoaeao niaea?aeaoue eiaeaen
ianyoea, ya eioi?ue n/eoaaony iieaoa.

Ia?aiaiioth G=0. Aeaiiay ia?aiaiiay niaea?aeeo eoiaiaoth noiio, eioi?oth
i?eaeaony caieaoeoue.

Ia?aiaiioth jc=0; Aeaiiay ia?aiaiiay ii?aaeaeyao eiaeaen oaeouaai
ianyoea iinea ia/aea ?aaiou.

Ia?aiaiioth q, eioi?ay ii?aaeaeyo a eaaeaeii ianyoea n ca?ieaoie iauai
inoathueony io aiciiaeiuo ?anoiaeia noiiu.

Oaa1. N/eoaai q eae

q= d1*jc^2+e1*jc+f1 – v1

Oaa2. N/eoaai noiio g, eioi?oth iaaei caieaoeoue a yoio ?ac. Iia
iaoiaeeoueny eae

g=Sic(1-p1′)^((t01+jc-ic)/12).

Oaa3. Anee q te oi eaeai ia oaa4 (inoaiia)

Anee ic>jc+t01 , oi ia?aoiae ia oaa ( iu ia iiaeai caieaoeoue ca ianyoe
?aiueoa, /ai ii ianooieo)

Ia?aoiae ia oaa 2 (ieaoei ca neaaeothuee ianyoe ec noiiu oiai aea
ianyoea)

Oaa4. oaaee/eaaai n/ao/ee ianyoea n ca?ieaoie

jc=jc+1

Anee jc > N-t01 ia?aoiae ia oaa5 (inoaiia, iu en/a?iaee ana ianyoeu n
iieo/aieai ca?ieaou)

Ia?aoiae ia oaa1

Oaa5. inoaiia. A aeaiiii ianoa a ia?aiaiiie G aoaeao cia/aiea, eioi?ia
/aeiaae caieaoeo ?iaenoaaiieeai.

Caia/aiea ii aeai?eoio:

Aiciiaeia neooaoeey, eiaaea /aeiaae o?aoee ia eo?nu aieueoa, /ai ii
iieo/aao aeaiueae, e noiia aeieaa ii e?aaeeoo ?anoao auno?aa, /ai
ca?ieaoa. Yoio neo/ae iiaeii iaia?oaeeoue ii neaaeothuei i?eciaeai:
jct02, oi aeiaaaei a iiiaeanoai S (te-t02) iauaeoia n ioeaaui
cia/aieai; i?e yoii noaiao te=t02. Iinea aeaiiiai oaaa aeiaaaei e
eaaeaeiio Si aaee/eio iinoiyiiuo ?anoiaeia f02.

I?aia?acoai iiiaeanoai S ( aiciiaeiiai oaaee/ea aai ?acia?iinoue). Anee
te>t12, oi aeiaaaei a iiiaeanoai S (te-t12) iauaeoia n ioeaaui
cia/aieai; i?e yoii noaiao te=t12. Iinea aeaiiiai oaaa aeiaaaei e
eaaeaeiio Si i?eoiaeyuaiony ia n?ie iieaou o/aau AOCa ?acia? iieaou
eioa?aaea o/aau. Yoio i?ioeann iiaeao auoue i?aaenoaaeai oi?ioeie

Si = Si+W, i=t11+nl… l=1..U.

Iinea aeaiiie i?ioeaaeo?u iaoiaeyo noiia?ioth noiio, eioi?oth i?eaeaony
caieaoeoue e?aaeeoothuaio eeoeo:

Aeai?eoi iaoiaeaeaiey noiiu, caiea/aiiie ii e?aaeeoai

Aa?ai ia?aiaiioth t=t12+t02+1. yoi aoaeao ia/aeueiue iiiaio a?aiaie.

Ia?aiaiioth ic=0. Aeaiiay ia?aiaiiay aoaeao niaea?aeaoue eiaeaen
ianyoea, ya eioi?ue n/eoaaony iieaoa.

Ia?aiaiioth G=0. Aeaiiay ia?aiaiiay niaea?aeeo eoiaiaoth noiio, eioi?oth
i?eaeaony caieaoeoue.

Ia?aiaiioth jc=0; Aeaiiay ia?aiaiiay ii?aaeaeyao eiaeaen oaeouaai
ianyoea iinea ia/aea ?aaiou.

Ia?aiaiioth q, eioi?ay ii?aaeaeyo a eaaeaeii ianyoea n ca?ieaoie iauai
inoathueony io aiciiaeiuo ?anoiaeia noiiu.

Oaa1. N/eoaai q eae

q= d2*jc^2+e2*jc+f2 – v2

Oaa2. N/eoaai noiio g, eioi?oth iaaei caieaoeoue a yoio ?ac. Iia
iaoiaeeoueny eae

g=Sic(1-p1′)^((t02+t12+jc-ic)/12).

Oaa3. Anee q te oi eaeai ia oaa4 (inoaiia)

Anee ic>jc+t02+t12 , oi ia?aoiae ia oaa ( iu ia iiaeai caieaoeoue ca
ianyoe ?aiueoa, /ai ii ianooieo)

Ia?aoiae ia oaa 2 (ieaoei ca neaaeothuee ianyoe ec noiiu oiai aea
ianyoea)

Oaa4 oaaee/eaaai n/ao/ee ianyoea n ca?ieaoie

jc=jc+1

Anee jc > N-t02-t12 ia?aoiae ia oaa5 (inoaiia, iu en/a?iaee ana ianyoeu
n iieo/aieai ca?ieaou)

Ia?aoiae ia oaa1

Oaa5. inoaiia. A aeaiiii ianoa a ia?aiaiiie G aoaeao cia/aiea, eioi?ia
/aeiaae caieaoeo ?iaenoaaiieeai.

Caia/aiea ii aeai?eoio:

Aiciiaeia neooaoeey, eiaaea /aeiaae o?aoee ia eo?nu aieueoa, /ai ii
iieo/aao aeaiueae, e noiia aeieaa ii e?aaeeoo ?anoao auno?aa, /ai
ca?ieaoa. Yoio neo/ae iiaeii iaia?oaeeoue ii neaaeothuei i?eciaeai:
jc

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