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Model of economics - Vіtlіnsky V.V.

10.3. Monitoring of the stochastic dynamics of the financial resource of the commercial bank

The food was stimulated by the multiplicatively stochastic model of visibility; more accurate forecasts for the hourly forecasting period, which is characterized by unremarkable minds.

Zvidsi has become an urgent task once more divided into methods of efficient and effective visualization of the moment of the official record, so that the resource is dynamically integrated (the moment of the moment is?, S2). Vaughn can be but rozvyazana for rachunok monitoring (postіynogo vіdstezhuvannya) value of mathematical method that dispersion vipadkovih oddities elementary transition .

The value of mi is the value of the available resource at the time of transition at the time of the hour t = i - 1 until the start time t = i : if m i <1 ( m i> 1), then it is possible to characterize the change (more) to the resource, and if mi = 1 , then the suttvih zmіn oath will not be transferred to the resource. Dispersion Visiting a step of undetermined value of a resource and servicing it for estimating a step of financially-economical operations, which is necessary to take an oath of resources.

Oskilki mathematically


і dispersion


vipadkovogo koefіtsієnta elementary transition unambiguously interchange with parameters

, (10.49)


vіdpovіdno vipadkovoї, divided by the normal law of magnitude then monitoring parameters can reduce to the mathematical model of m i that dispersion , which is subordinate to the normal law of vipad values, for which a large arsenal of statistics has been scattered. Otzhe, for health monitoring parameters stochastic dynamics of the resource, you can submit such a scheme:

Nekhay system analytic sposter_gaє low last-day value oath resource x 0, x 1, ..., xn . Vvazhayuchi, scho all the value of nevid'mnі, I will enumerate the low value a1, ..., a n :

With a multiplicative stochastic model of dynamics of a resource, a low value is ln a i , i = 1, ..., n can be interpreted as a series of one-time realizations of an independent normally distributed vipadkov value .

To monitor the mathematical method (trend) of a whole row, you can, for the most part, use a middle-order k- order. , I will be counted for by the formula:


for the moments at the hour i = k , k + 1, ..., n . Similarly, kovzna dispersion k- th order


de i = k , k + 1, ..., n . Pіdstavlyayuchi (10.51), (10.52) for the formula (10.47), (10.48), we can remove the shirak shukanih indoor estimates for the mathematical calculation of the dispersion of the vipadka odds of the ith elementary transition :


i = k , k + 1, ..., n . (10.54)

As a matter of fact, let’s secure, let it be at the moment t = 0 є a single oath to the resource ( x 0 = 1), then the quantity maє zmіst oath to the resource at the time t = i.

One way to monitor the stochastic dynamics of the resource є own now and again (parameter_v ) prices dynamic. In a simple vipadu taku zmіnu you can give a yak perekhid vid a number , which is n 1 times the normalization of normally distributed value up to a number scho become n 2-fold realizatsiyu normally distributed vipadkovo value .

Let’s let it go, but the dispersion of these two rows is far apart. , then reinterpretation of the statistical hypothesis of the equality of mathematical methods Zdіsniti for the additional student criterion is possible:



. (10.56)

Zafіksuvshi іvіn dovіri b I (0,1) chi ryvn allowable rziziku (g = 1 - b) for the maximum number of hypotheses H 0: m1 = m2 th calculating the most critical value T (b; g) for the criterion of student + n = n n 2 - 2 steps of freedom, take into account the hypothesis of H 0 for think і відхиляємо цю hypothesis for the alternate H 1: m1> m2 (chi for alternate H 2: m1 <m2 - fall in the form of the sign of the value T ( n 1, n 2) per mind )

I have outlined the procedure for showing statistically significant changes in the parameter m that can be included in the main scheme for monitoring the resource.

For the moments at the hour i = k , k + 1, ..., n , the “covenant" of Student's t-shirt is counted:




і for the value i = 2 k , 2 k + 1, ..., n , the hypothesis H 0 is reinterpreted for the optional student criterion with n = 2 ( k - 1) steps of freedom.

The procedure for rewriting a statistical hypothesis is H 0: m1 = m2 for the optional student criterion, you can expand it on a vipadoc of irregular dispersions . The number of times to show is that for the irregular dispersion of the pre-school students criterion of students with the highest degree of freedom n, they should lie in the interval from k - 1 to 2 ( k - 1).

Similarly conducted dispersion monitoring for periodically changing the number of hours for equal dispersion in the middle, do not overthrow in the middle of the hour. For the whole "kovzniy" other dispersion is counted:


for the moment .

Yakshcho zafіksuvati step permissible rziku g (chi rіven dovіri b = 1 - g) de - post_yna dispersion of vipadkovyh values , a - post_yna dispersion of vipadkovyh values , then the hypothesis H 0 is possible to convert the calculated values ​​of F ( i , k ) to the critical values F -criterion with steps of freedom .