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Model of economics - Vіtlіnsky V.V.

10.5. Bagatoetapna dynamics of financial resources on the basis of multiplier multiplicative stochastic models

* 6

* 6: {Konyukhovsky P.V. Microeconomic modeling of banking. - St. Petersburg: Peter, 2001.}

Rozglyanmo seems to be a simple situation. Dearly, the oaths of the healed mischief (koshtiv) for the periods of the current official, the dynamics of which can be described for the help introduced in Section 10.2. multiplicative stochastic model.

An oath of healed koshtіv at period t + 1

(10.64)

de somefrost_growth - vipadkovі magnitudes, raspodіlenі zgіdno with lognormalnom law iz parameters m i that s i . Let yourself go, then m i to lie down vid ( ) Otzhe, Rivnyannya (10.62) Matime Viglyad:

. (10.65)

Razv'yazok given rivnyannya possible v_dshukati, victorious method of Duhamel for Z- reconfiguration. For the sake of the most important, additional assistance:

gt +1 - r gt = d t , g 0 = 0, (10.66)

de

(10.67)

Nekhai gt ® G ( z ) і d t ® 1 - Z- interchange of functions gt і d t . Todd gt +1 ® ZG ( Z ), and the image is rivnian for (10.66) matime wiglyad:

(10.68)

Ozhe

(10.69)

Original for

seniority rt. Mamo z vіdomih authorities Z- redefinition:

(10.70)

Shchob bring rivnyannya (10.65) to zero on the other hand, introduce a new ht = qt - q 0. Yakshcho let, sch

(10.71)

then rivnyannya for type in the look:

(10.72)

P_slya low rebirth know, shcho

. (10.73)

In this way, the mother’s separation of the sacrifice of religion (10.65):

(10.74)

Yakshcho koofіtsі одnti elementary transition may have the same signs for all moments , ros'vyazok (10.74) when I look:

(10.75)

Victory results, rejected for the support of stochastic multiplicative models, prediction of oaths of healed koshtіv at the moment t + 1 matima viglyad:

(10.76)

de x 0 - the oath of the healed bags at the ears ( t = 0); - Estimates of the value of the parameters m, s відповідно.

It’s probably because of the relative independence of the transition, it’s replaced by the formula (10.75) with the latest estimates, we’ll take away the forecast for the estimated value of the total cost of the moment:

(10.77)

de It is possible to primatize (10.76).

In okremoy vipadka, yakshko , pіslya rozkrittya negligible Viraz (10.77) matime bіlsh compact form:

. (10.78)

Formulas (10.77) and (10.78) may be read more economically Interpretation is an oath of the highest cost of financial companies at the time t to lay down two storage rooms (at the boundaries of the formed model):

  • q 0 r t - the size of the cob capitulum with urachuvannia accumulation policy;
  • - the result of dyalnosty shochod hellishly kotіv that rivimannya income in the form of active and regional victorious ix.

You can hello graph ustroystry "behavior" last One hundred percent of the value of normi vitrate for healing cost ( v ).

Give it a shot for demonstrating the meanings of the methods on the conceptual level.

For a statistical database, I’m willing to pay financial attention to the Bank of New York (USA), you can choose to use the FDIC Web server. So, at table. 10.1 to pay tribute to the dynamics of vigorous capital, goiters and other income from the entire bank (in millions of US dollars) for the period 1992-1997 rocky. Table 10.1

DYNAMICS OF VLADNY KAPITALU, ZOBOV'YAZAN, VIDOTOKOVYKH REVENU I I VITRAT BANK NEW YORK FOR 1992-1997 rubles, million dollars *

Rik

Zobov'yazannya,

Vlasny capital,

Vіdsotkoviy dohіd,

Vіdsotkovі Vitrati,

Chistiy vіdsotkoviy dohіd,

1992

34038

2606

2065

1131

934

1993

33207

2881

1808

836

972

1994

36226

3062

2087

1030

1057

1995

39225

3487

2634

1447

1188

1996

48096

4025

2785

1419

1366

1997

51193

4961

3093

1599

1494

* html: www.fdic.gov

On the previous table. 10.1 knowable estimates value of income standard yak averaged view of income-generating income Ut to the full capital xt + qt і normi vitrat on third generation , scho to increase the average appearance of the Votdsky Vitrats Vt to the oath of the goiter and the anterior period xt –1.

Urakhovucci, right now I’m looking for good officials, since I’ve got a good income and a good deal, I’ve got to pay a fee, I need to introduce a normal rate of increase in capital gains Pislya polnogo on ny of the first initial estimates of income standards and vitrat otrimaєmo otsіnki . Victoristovy for the valuation of the value of the elementary transition to obzagіv zobov'yazan formula (10.76) і підставляючи deputy u that v otsіnki ikh that at the formula (10.77), it is possible to express the predicted value of the liabilities of the lofty capital on the rocks of the rosy-eyed period. The results were presented at the table of the table (Table 10.2).

Table 10.2

ACTUAL FORECAST FORECAST VALUE OF VLADIMARY CAPITAL BANK NEW YORK, mln USD *

Rik

Zobov'yazannya,

Vlasny capital is a fact

Vlasny capital - forecast,

Zokrem

Vidkhilennya forecast vid fact, %

1992

34038

2606

-

-

-

-

1993

33207

2886

3053

2609

445

–6.0

1994

36226

3062

3541

2612

939

–15.7

1995

39225

3487

4072

2615

1457

–16.8

1996

48096

4025

4651

2618

2033

–15.6

1997

51193

4961

5281

2621

2660

–6.5

* Rozrakhunok is given for the given html: www.fdic.gov Acceptably vidpovidno Q = 0,05, r »1,001.

It is clearly a high rivie nthilenzh between pinkhunk and actual obediem adequate to the rivine of the bribe laid down by the Vikings.

Rosvivati ​​vladeniya vishche pіdkhіd possible, for example, such an order. For the sake of vivacity, there is a great deal of opportunity to have a good time for the most important things to do.

For pobudovi prognozіv ochіkuvanih values ​​obsyagіv fіnansovih resursіv depozitnoї Nature, akumulovanih for rakhunok koshtіv znachnoї kіlkostі vkladnikіv (Homogeneous rahunkіv) mozhut Buti vikoristanі stohastichnі modelі bankіvskih depozitіv have yakih a basis we can take gіpotezu schodo mozhlivostі inventory protsesіv, SSMSC zumovlyuyut zmіnu kіlkostі rahunkіv i kіlkostі the operation with them for the auxiliary vipadovyh values, the subordination of the law of Poisson, and the number of vnidnoshnogo zmіni rahunkіv at the end of the window; the operation - for the auxiliary vipadkovi x quantities, scho mayu lognormalny law rozpodilu.