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Modelyuvannya Economy - Vіtlіnsky VV

10.2. Banks that stochasticity modelyuvannya fіnansovih potokіv

10.2.1. Osnovnі kontseptsії stochasticity modelyuvannya fіnansovih potokіv

Yak zovnіshnі minds scho vplivayut on dіyalnіst komertsіynogo Bank (chi fіnansovoї fіrmi), so i processes scho rozvivayutsya from the bank itself, Yea result skladnoї i neodnoznachnoї vzaєmodії bagatoh chinnikіv, reasons, fallow, bagato s yakih Got vipadkovu (ymovіrnіsnu) i / chi nechіtku (rozplivchastu) nature. Naslіdkom tsogo Yea those scho robot bankіvskoї place the digit mіroyu obtyazhena neviznachenіstyu that zumovlenim her rizikom.

One Zi sposobіv for Relief yakogo mozhna opisati threading mill jar (chi іnshoї fіnansovoї іnstitutsії), Je Opis Yogo for Relief characteristics of the vector:

x = (x 1, ..., xn).

Kіlkіsny that yakіsny warehouse component of the vector x viznachaєtsya detalіzatsії stage.

Tsya factual inventory will form the bank for zmіstom bankіvskomu adequate balance: the components of the vector x mozhut Buti yak іnterpretovanі zvichaynі stattі balance and Quantity їh i yogo structure vіdpovіdayut rіvnyu agregovanostі (schodenny - yaky vklyuchaє rahunki another order, chi uzagalneny - Quarterly toscho). Konkretnі kozhnoї values xj z component of the vector x will viznachayutsya obrannyam odinits vimіryuvannya for vіdpovіdnogo resource (information). Zdebіlshogo tse vimіryuvachі koshtіv in tіy chi іnshіy valyutі; Buti shaping can i so zvanі resursnі odinitsі (p. od.). Stan okremogo j-th resource ototozhnyuєtsya s deyakim Elements mnozhini nevіd'єmnih dіysnih numbers , Geometric way yakoї Je dodatna pіvvіs dіysnoї chislovoї osі. Otzhe, mill jar zagalom mozhna taxes deyakoyu point nevіd'єmnogo orthant n- mіrnogo evklіdovogo expanse:

Mnozhina vsіh mozhlivih (permissible) tochok (vektorіv) x utvoryuє Prostir stanіv bank:

Mozhut stvoryuvatisya takozh pevnі pohіdnі (vtorinnі) characteristics:

Zaznachimo scho vector pohіdnih characteristics Je funktsієyu od vector x: y = f (x) .

Yak butt types pohіdnih (vtorinnih) characteristics will postaє bank system obov'yazkovih fіnansovih normativіv (koefіtsієntіv), scho їh ustanovlyuyut tsentralnі banks chi INSHI regulyuyuchі bodies.

For vrahuvannya chinnika hour potrіbno zadati deyaku mnozhinu T Elements kotroї t I T nazivayut moments hour. Traditsіyno yak model "neperervnogo fіzichnogo" hour vikoristovuyut mnozhinu tochok neskіnchennoї odnomіrnoї dіysnoї chislovoї osі R 1 of fіksovanim cob vіdlіku and mnozhina vsіh urahovuvanih momentіv hour T - tse Pevnyi vіdrіzok on tsіy osі.

Yakscho given model neperervnogo hour, the camp j -ї characteristics can rozglyadati yak funktsії values xj (t), at scho viznachena mnozhinі T i nabuvaє value on mnozhinі . Grafіk funktsії xj (t) vіdіgraє role traєktorії zmіni in chasі j -ї characteristics. Stan bank zagalom - tse values ​​vektornoї funktsії hour:

(10.13)

and traєktorіya Sistemi Je deyakoyu curve (gіperpoverhneyu) in n -mіrnomu prostorі.

Viznachaєtsya TAKE ponyattya takozh, yak "potіk".

Potіk - tse Ekonomichna value KOTRA vimіryuєtsya in rusі s urahuvannyam rozglyaduvanogo іntervalu hour. Rozmіrnіst flow - tse obsyag, podіleny on іnterval hour.

Zmіstovny bіk ponyattya "potіk 's pov'yazany ponyattyam shvidkostі zmіni camp system.

Yakscho pripustiti scho funktsії xj (t), scho zadayut traєktorії zmіni characteristics become bank Je smooth that diferentsіyovanimi access in all points іntervalu T = (T - T +), then vіdpovіdnі Pershi pohіdnі

(10.14)

mozhna іnterpretuvati yak shvidkostі zmіni Tsikh characteristics. Rozglyadayuchi specific resources otrimuyut vіdpovіdnі Vidi potokіv: fіnansovy, Penny, potіk gotіvki toscho.

Dinamіka bank in tsіlomu Mauger Buti described for the Relief of the vector of resource flows

yaky zadaє vector shvidkostі zmіni will doslіdzhuvanogo ob'єkta in prostorі.

Meaning okremoї characteristics ob'єkta doslіdzhennya to whether yakogo hour time t I (T -, T + ) viznachaєtsya of the formula:

(10.15)

Formuєtsya takozh model ґruntuєtsya yak yak on vіdobrazhennі Bank System (vector) Pervin resource potokіv:

. (10.16)

Analogіchno mozhna rozglyadati i pohіdnі (vtorinnі) resursnі flows:

. (10.17)

Obidvі s guidance models ((10.13) that (10.16)) give uyavlennya schodo camp bank for an hour skin time t. However, you can bring low prikladіv, if vinikaє neobhіdnіst in perehodі od "of point" filed to "іntegralnogo" inventory povodzhennya j- ¯ performance on tasks Pevnyi іntervalі hour

. (10.18)

For tsogo administered ponyattya serednogo property value (j- ¯ vector components will) on іntervalі (t -, t +):

(10.19)

yak vimіryuєtsya in vіdpovіdnih resource odinitsyah and takozh serednogo flow:

(10.20)

scho vimіryuєtsya in resource odinitsyah on odinitsyu hour. Zaznachimo scho (10.20) viznachaє serednyu shvidkіst zmіni obsyagu j- th resource for іnterval (t -, t +).

Modelі dinamіki bankіvskih resursіv scho ґruntuyutsya on neperervnomu podannі hours іntervalіv not Povny mіroyu vіdpovіdayut processes, SSMSC realіzuyutsya on praktitsі. According au-Perche, "fіzichny hour" yak Taqiy, scho i Pliny rіvnomіrno neperervno not vіdpovіdaє zazvichay vnutrіshnіm rhythms "zhittєvogo cycle" ekonomіchnih sub'єktіv. Klasichny butt nevіdpovіdnostі "fіzichnogo" i "ekonomіchnogo 's hour pov'yazany neobhіdnіstyu vrahuvannya vihіdnih i Svyatkovyy dnіv, uprodovzh yakih banks do not vikonuyut svoї operatsії. Alternatively, neperervnіst visuvaє visokі vimogi schodo masivіv danih, neobhіdnih for vіdpovіdnogo їh testuvannya that ekspluatatsії.

To go od neperervnogo hour to discrete, scho bіlsh adequately vrahovuє minds dіyalnostі fіnansovo-ekonomіchnih іnstitutіv, Mauger vikoristovuvatisya since been called to come іntertemporalna Hіksa model * 3. Zgіdno s tsієyu kontseptsієyu skіnchenny vіdrіzok hour [t -, t +], vprodovzh yakogo sposterіgaєtsya funktsіonuvannya doslіdzhuvanoї system podіlyaєtsya on rіvnі K Chastain (vіdrіzki that napіvіntervali) dovzhinoyu d:

* 3: {Hіks J. Value and Capital.. - M., 1993.}

de

In this osnovі podіlu - gіpoteza for yakoyu vseredinі Tsikh іntervalіv usі parametric xj (t), scho mill harakterizuyut bank that minds Yogo funktsіonuvannya, zalishayutsya (nablizheno) postіynimi i zmіnyuyutsya deprivation in the furrows іntervalіv hours. Tsya іdeya on printsipovomu rіvnі zobrazhena in Fig. 10.1.

Fig. 10.1. Perehіd od neperervnogo hour before in discrete іntertemporalnіy skhemі Hіksa

Otzhe, otrimuєmo discrete "bankіvsky" h t, scho pribiraє values 0,1, ..., k, ..., K. Easy zdіysniti uzagalnennya, vrahovuyuchi those scho moments "bankіvskogo" t hour vіddіlenі promіzhkami hour rіznoї dovzhini. Tse dozvolyaє vrahovuvati bіlsh exactly vimogu postіynostі protsesіv useredinі Tsikh vіdrіzkіv that chinnik vihіdnih i Svyatkovyy dnіv.

For discrete vprovadzhennya hour vіdbuvaєtsya fіksatsіya vіdnosno yogo momentіv vektorіv will (vihіdnih characteristics):

x (t) = (x 1 (t), ..., x j (t), ..., xn (t))

that vektorіv resource potokіv:

Mozhna takozh go od "schodennogo" hour to "schotizhnevogo", "schomіsyachnogo" toscho.

Krok in the following protsesі vdoskonalennya rozglyaduvanogo class models - urahuvannya them chinnikіv neviznachenostі that zumovlenogo riziku them. For tsogo zruchno skoristatisya termіnologієyu teorії vipadkovih protsesіv. Pid vipadkovim (stochastics) Process (vipadkovoyu funktsієyu hour) rozumіyut funktsіyu x (t), KOTRA Mauger mother of the chi іnshu specific realіzatsіyu (traєktorіyu) s deyakoї fіksovanoї mnozhini mozhlivih traєktorіy:

Otzhe in the minds neviznachenostі Modell dinamіki will bank Mauger sluguvati Vector vipadkovy processes:

cutaneous component yakogo opisuє stochasticity dinamіku j -ї characteristics (resource) to the bank. Analogіchno chinnik neviznachenostі, nayavny in sistemі resource potokіv bank can have opisati formalіzovanomu viglyadі for Relief vector vipadkovogo processes:

Doslіdzhennya, spryamovanі on zmіstovny analіz zakonomіrnostey funktsіonuvannya bankіv, toil spiratit on danі that gіpotezi scho konkretizuyut type i parametric vikoristovuvanih vipadkovih funktsіy values ​​i * 4.

* 4: {Hovanov NV Mathematical models of risk and uncertainty. - Saint Petersburg, 1998}.