Risk Analysis Technology of Regional Systems on the Base of Statistical Rates

Risk Analysis Technology of Regional Systems on the Base of Statistical Rates

Katheryna ZaslavskaFaculty of Cybernetics Kyiv National Taras Shevchenko University Department of System Analysis and Decision-Making Theory

Information and Technology in the Knowledge Era

Risk Analysis Technology Outline


Actuality

Rating and risk

Regional systems

Problem investigation

Laws

Data

Mathemetical tool

System of risk calculation

Mathematical models and optimization

Data analysis

Multicriterion approach for measurement of the strategic risk

Conclusions

Actuality


Monitoring, estimation of region condition are connected with neessity of identification of depressive territories and creation of goal-directed financial and technological support for territories, leading them out of crisis.

In work analysis of territory depressiveness is produced with using of ordinal method of risk study on base of known ratings for system elements.



Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions

Rating and risk


Rating is numerical or ordinal index, reflects importance or meaning of certain object or event. Examples are:

Popularity degree of famous figure (in politics, culture)

Rating of popular sites with using WEB 2.0. technology

Quoting index of scientific articles and web-resources

Ratings are important for simultananeous conducting of situation, because with the help of ratings you may analyze data just for certain period.

The integral parts of rating are factors, on base of which it is formed. In given work such factors are risk values of regions and areas of Ukraine.

Rating and risk


The notion of the risk concerns with understanding of the dangers, threats, unreliability, uncertainties, accidents, damage.

Term "risk" derives from Latin word resecum rock or the danger of the collision with her.

In economic literature theoretical determination of notion risk is following statement, according to which risk in its fundamental principle is an uncertainty.

The factor of risk for its contents it is not only probability of the appearance of the casual event (unsure), but also probability of the coming the negative result.



Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions

Regional systemsFinancial systemsPayment systems Banking systems Large corporations Regional systems


Main task while investigation such systems - investigation of risk of the whole system.

Each systems element makes contribution to:

system effective functioning,

life support (security)

It has certain risks that may lead to dangerous conditions for system.

In this work an approach to system risk investigation on base of known ratings for system elements is considered.

Ratings are used while investigation of banks risks that consist of subdivisions, countries risks through regions conditions and transnational companies, through conditions of subdivisions.



Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions

Problem investigationTechnologies for problem investigation:Laws,rulesDATAWith the help of all this elements we will be able to get as a result a list of depressive territories.

Mathematical tool



Laws


Legal base of regional development level classification, industrial regions, agricultural regions and cities of regional (republican in Crimea) importance is Ukraine law Of stimulation regional development (Statements of Verkhovna Rada of Ukraine.-2005.-51.-p.548)

Groups of territories:

Regions (Crimea, 24 regions, Kiev, Sevastopol)

Industrial regions

Agricultural regions

Cities of regional

importance

DataRegions can be stable,but some of them not


1

Gross domestic product for 1 person (in actual prices), grn.

20042005

rankvalueW-coef.rankvalueW-coef.

Crimea1749510.9271764600.923

Vinnickiy2147000.942159660.944

Volynskiy2047710.9361962850.93

Dnipropetrovskiy486090.743119090.698

Doneckiy297130.6842124900.674

Zhitomerskiy2443970.9552455540.961

Zakarpatskiy2542380.9632553730.968

Zaporozhskiy580930.7675106830.749

I-Frankovskiy1352380.9121269160.904

Kievskiy866520.84786730.832

Kirovogradskiy1551220.9181863940.926

Luganskiy1059730.875981310.854

Lvovskiy1253960.9041466570.915

Nikolaevskiy964240.8521078010.868

Odesskiy770280.821886190.834

Poltavskiy388410.7294115740.712

Rovnenskiy1948170.9342062690.931

Sumskoy1650090.9241564970.922

Ternopolskiy27351612746031

Harkovskiy671820.813690250.817

Hersonskiy2345460.9472357130.954

Hmelnickiy2245490.9472257640.952

Cherkaskiy1848530.9321366810.914

Chernoveckiy2635890.9962646540.998

Chernigovskiy1451630.9161664740.923

Kiev (city)12313001287800

Sevastopol (city)1158470.8811174520.882

Mathematical tool. Methods of investigationSystems analysisMethods of decision-makingStatistical analysisVisualizationSoftware




Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions



Regional system contains n subdivisions, for them in time periods

ratings are defined.

describes observations of subdivisions behavior,

by columns defined subdivisions ratings (ordinal numbers) in fixed time period.

-incidence matrix,

indicate the number of times subdivision

move from state

to state

in period of

.

describe transitions between states of territorial-distributed systems, elements are summed elements of matrix

.

- transition matrix,

- conditional probabilities

- sum of the rows of this matrix.

_1314040800.unknown

_1314607078.unknown

_1314607236.unknown

_1314607442.unknown

_1314607522.unknown

_1314607574.unknown

_1314607404.unknown

_1314607094.unknown

_1314040880.unknown

_1314607032.unknown

_1314040865.unknown

_1287167675.unknown

_1287167684.unknown

_1287167658.unknown



The average conditional entropy

of system is:

=

,

expresses the amount of information contained in observations on the system if the present subdivisions positions are known.

-expresses the relative uncertainty of the system or risk in system,

. Generalization of system is achieved with using of weighted entropy. Weights for risk:

, a -the constant of proportionality, - the marginal weight assigned to holding position.

- weighted average conditional entropy, that represents the strategic uncertainty of the payment system.

_1314607791.unknown

_1314607967.unknown

_1314608883.unknown

_1314608967.unknown

_1314608854.unknown

_1314607836.unknown

_1314607705.unknown

_1314607721.unknown

_956858112.unknown



The maximum weighted entropy

is found out as the solution of the mathematical programming problem:

under constraints

The relative weighted average conditional entropy

:

represents the degree to which a system is uncertain when the decision makers' value structures are incorporated as a system of weights.

_1314607982.unknown

_1314608285.unknown

_1314608414.unknown

_1314608459.unknown

_1314608293.unknown

_1314608252.unknown

_983636972.unknown

Table 1. Rating of Ukrainian regions by extra cost


1

121710

171121

222914

141017

121710

191520

1

Extra cost

2000200120022003200420052006

1Crimea21201816171715

2Vinnickiy17131718212121

3Volinskiy18192020201920

4Dnipropetrovskiy3333433

5Doneckiy4222222

6Zhitomerskiy20242425242424

7Zakarpatskiy25252524252525

8Zaporozhskiy2455555

9I-Frankovskiy15171413131214

10Kievskiy6889877

11Kirovogradskiy2314161715188

12Luganskiy111212121099

13Lvovskiy14161311121412

14Nikolaevskiy10991091011

15Odeskiy7666788

16Poltavskiy5544344

17Rovnenskiy16181919192017

18Sumskoy9111114161516

19Ternopolskiy26262727272726

20Harkovskiy8777666

21Hersonskiy22222123232323

22Hmelnickiy19232221222222

23Cherkaskiy13212322181313

24Chernoveckiy27272626262627

25Chernigovskiy12151515141619

26Kiev (city)1111111

27Sevatopol (city)2410108111110

Table 2. Incidence matrix for period 2000-2004


1

121710

171121

222914

141017

121710

191520

1

Matrix 2000-2004

123456789101112131415161718192021222324252627

15

241

341

41121

514

6311

723

81211

91211

10122

11221

12131

131211

14113

15131

161121

1711111

181121

19311

20131

211112

22122

23122

24122

2523

2641

2714

Table 3. Transition matrix for period 2000-2004


1

121710

171121

222914

141017

121710

191520

1

123456789101112131415161718192021222324252627

11

20.80.2

30.40.2

40.20.20.40.2

50.20.8

60.60.20.2

70.40.6

80.20.40.20.2

90.20.40.20.2

100.20.40.4

110.40.40.2

120.20.60.2

130.20.40.20.2

140.20.20.6

150.20.60.2

160.20.20.40.2

170.20.20.20.20.2

180.20.20.40.2

190.60.20.2

200.20.60.2

210.20.20.20.4

220.20.40.4

230.20.40.4

240.20.40.4

250.40.6

260.80.2

270.20.8



Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions

Data analysis


In table 2 incidence matrix for investigation period 2000-2004 years is represented. Incidence matrix was formed on the base of table 1.

On table 3 transition matrix is represented. This table was formed on the base of table 2. On the base of table 3

values were calculated:

for period 2000 2004 years:

= 0.96099


= 0.99755


= 1.05057

=3.29584


=0.29158


=0.30267


=0.31876

_1314647883.unknown

_1314647932.unknown

_1314648050.unknown

_1314648096.unknown

_1314648207.unknown

_1314648223.unknown

_1314648073.unknown

_1314648041.unknown

_1314647900.unknown

_1314647919.unknown

_1314647893.unknown

_1314647865.unknown

_1314647874.unknown

_1314647834.unknown

Pic.1.Value of system risk Results of calculation of system risk in Ukraine for period of 2000-2006 years presented in diagramFor period 2000-2006 system risk increased on 10%.


1

0.29158

0.30267

0.31876

System risk

System risk

1

20002001200220032004risk

1 21201816170.0169719

217131718210.178831

318192020200.076576

4333340.059610

542222023

620242425240.076577

725252524250.0169720

8245550.119223

9-15171413130.059611

10688980.119224

1123141617150.022617

1211121212100.0169721

1314161311120.022618

1410991090.059612

15766670.059613

1655443024

1716181919190.076578

189111114160.12492

1926262727270.059614

2087776025

2122222123230.0169722

2219232221220.119225

2313212322180.076579

242727262626026

2512151515140.059615

26.11111027

27.2410108110.059616

123456789101112131415161718192021222324252627

515

5241

5341

541121

5514

56311

5723

581211

591211

510122

511221

512131

5131211

514113

515131

5161121

51711111

5181121

519311

520131

5211112

522122

523122

524122

52523

52641

52714

H(kj)/ln27=0.29158H(k/j)=0.96099

123456789101112131415161718192021222324252627

111

120.80.2

130.40.2

140.20.20.40.2

150.20.8

160.60.20.2

170.40.6

180.20.40.20.2

190.20.40.20.2

1100.20.40.4

1110.40.40.2

1120.20.60.2

1130.20.40.20.2

1140.20.20.6

1150.20.60.2

1160.20.20.40.2

1170.20.20.20.20.2

1180.20.20.40.2

1190.60.20.2

1200.20.60.2

1210.20.20.20.4

1220.20.40.4

1230.20.40.4

1240.20.40.4

1250.40.6

1260.80.2

1270.20.8

200020012002200320042005risk

1 2120181617170.0205

21713171821210.1969

31819202020190.0411

43333430.0205

54222220

62024242524240.0862

72525252425250.0205

82455550.1313

9-1517141313120.0656

106889870.1313

112314161715180.0701

12111212121090.0205

131416131112140.0899

141099109100.0411

157666780.1313

165544340.0205

171618191919200.1067

18911111416150.135

192626272727270.0656

208777660

212222212323230.0205

221923222122220.1313

231321232218130.0862

242727262626260

251215151514160.0693

26.1111110

27.241010811110.0656

123456789101112131415161718192021222324252627

616

6251

6342

641221

6515

66411

67231

682211

691221

610132

611321

6121311

61311211

614114

6151311

61611121

61711121

61811121

619321

6201131

6211212

622123

623123

624132

62524

62651

62715

H(kj)/ln27=0.30267H(k/j)=0.99755

123456789101112131415161718192021222324252627

111

120.830.17

130.670.33

140.170.330.330.17

150.170.83

160.670.170.17

170.330.50.17

180.330.330.170.17

190.170.330.330.17

1100.170.50.33

1110.50.330.17

1120.170.50.170.17

1130.170.170.330.170.17

1140.170.170.67

1150.170.50.170.17

1160.170.170.170.330.17

1170.170.170.170.330.17

1180.170.170.170.330.17

1190.50.330.17

1200.170.170.50.17

1210.170.330.170.33

1220.170.330.5

1230.170.330.5

1240.170.50.33

1250.330.67

1260.830.17

1270.170.83

2000200120022003200420052006risk

1 212018161717150

2171317182121210.2185

3181920202019200.0442

433334330.0223

542222220

6202424252424240.0951

7252525242525250.0223

824555550.1456

9-151714131312140.0951

1068898770.1456

1123141617151880.1003

121112121210990.0223

13141613111214120.0498

14109910910110.1174

1576667880.1456

1655443440.0223

17161819191920170.1045

1891111141615160.2237

19262627272727260.0223

2087776660

21222221232323230.0223

22192322212222220.1456

23132123221813130.0951

24272726262626270.0223

25121515151416190.1508

26.11111110

27.24101081111100.0729

123456789101112131415161718192021222324252627

717

7261

7352

741231

7516

76511

77241

782311

791321

7101321

7111321

7121321

71311311

7141114

71513111

716111211

71711221

718111121

719331

72011131

7211312

722124

723124

724142

72525

72652

72725

H(kj)/ln27=0.31876H(k/j)=1.05057

123456789101112131415161718192021222324252627

111

120.860.14

130.70.3

140.140.30.430.14

150.140.86

160.70.140.14

170.30.570.14

180.30.430.140.14

190.140.430.30.14

1100.140.430.30.14

1110.140.430.30.14

1120.140.430.30.14

1130.140.140.430.140.14

1140.140.140.140.57

1150.140.430.140.140.14

1160.140.140.140.30.140.14

1170.140.140.30.30.14

1180.140.140.140.140.30.14

1190.430.430.14

1200.140.140.140.430.14

1210.140.430.140.3

1220.140.30.57

1230.140.30.57

1240.140.570.3

1250.30.7

1260.70.3

1270.30.7

2

123456789101112131415161718192021222324252627

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

20.1788311 0.0169719

180.1249220.178831

80.11922330.076576

100.11922440.059610

220.119255023

30.07657660.076577

60.07657770.0169720

170.07657880.119223

230.0765799-0.059611

40.059610100.119224

9-0.059611110.022617

140.059612120.016921

150.059613130.022618

190.059614140.059612

250.059615150.059613

27.0.05961616024

110.022617170.076578

130.022618180.12492

1 0.0169719190.059614

70.016972020025

120.016921210.0169722

210.0169722220.11925

5023230.076579

1602424026

20025250.059615

2402626.027

26.02727.0.059616

20.19691

180.13521 0.020518

80.1313320.19691

100.1313430.041116

150.1313540.020519

220.131365024

170.1067760.08629

130.0899870.020520

60.0862980.13133

230.0862109-0.065613

110.070111100.13134

250.069312110.070111

9-0.065613120.020521

190.065614130.08998

27.0.065615140.041117

30.041116150.13135

140.041117160.020522

1 0.020518170.10677

40.020519180.1352

70.020520190.065614

120.02052120025

160.020522210.020523

210.020523220.13136

5024230.086210

2002524026

24026250.069312

26.02726.027

27.0.065615

180.223711 024

20.2185220.21852

250.1508330.044216

80.1456440.022317

100.145655025

150.1456660.095111

220.1456770.022318

140.1174880.14564

170.104599-0.095112

110.100310100.14565

60.095111110.100310

9-0.095112120.022319

230.095113130.049815

27.0.072914140.11748

130.049815150.14566

30.044216160.022320

40.022317170.10459

70.022318180.22371

120.022319190.022321

160.02232020026

190.022321210.022322

210.022322220.14567

240.022323230.095113

1 024240.022323

5025250.15083

2002626.027

26.02727.0.072914

123

1

2

3

4

5

6

7

8

9-

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26.

27.

1 0.01697191 0.0205181 024

20.17883120.1969120.21852

30.07657630.04111630.044216

40.05961040.02051940.022317

502350245025

60.07657760.0862960.095111

70.016972070.02052070.022318

80.11922380.1313380.14564

9-0.0596119-0.0656139-0.095112

100.119224100.13134100.14565

110.022617110.070111110.100310

120.016921120.020521120.022319

130.022618130.08998130.049815

140.059612140.041117140.11748

150.059613150.13135150.14566

16024160.020522160.022320

170.076578170.10677170.10459

180.12492180.1352180.22371

190.059614190.065614190.022321

200252002520026

210.0169722210.020523210.022322

220.11925220.13136220.14567

230.076579230.086210230.095113

2402624026240.022323

250.059615250.069312250.15083

26.02726.02726.027

27.0.05961627.0.06561527.0.072914

123

1

2

3

4

5

6

7

8

9-

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25-

26.

27.

.

.

2

1

3

1

2

2

3

3

1

2

3

123

0.291580.302670.31876

Pic.2 Regions risk in 1 period 2000-2004We may see most riskyregions:

Vinnickiy Sumskoy Zaporozhskiy


Pic.3 Regions risk in 2 period 2000-2005


Pic.4 Regions risk in 3 period 2000-2006




Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions



Criteria, that were used in risk calculating for industrial regions:

Average monthly salary of 1 hired worker

Volume of industrial product sold

Understanding the importance degree of determined criterion in certain situation for analysis region depressiveness, it is necessary to assign him determined weight. We take weight as

,

.

- risk types for regions on given criterions (

- amount). General risk for region -

Using this formula we have counted the risk for industrial regions of Kiev area.

List of industrial regions of Kiev area:

1.Boguslavskiy

2.Borodyanskiy

3.Vasilikovskiy

4.Vishgorodskiy

5.Ivankivskiy

6.K-Svyatoshinskiy

7.Makarivskiy

8.Mironovskiy

9.Obuhovskiy

10.Skvirskiy

_1305360942.unknown

_1305360944.unknown

_1305360945.unknown

_1305360943.unknown

_1305360941.unknown

Pic.5. Risk when


Criterion weights were equal:

.

_1305360937.unknown

Pic.6. Risk when and


Criterion weights were different: criterion weight of industrial product

, criterion weight of salary

.

_1305360934.unknown

_1305360935.unknown

Pic.7. Risk when and


Criterion weights were different: criterion weight of industrial product

, criterion weight of salary

.

_1305360931.unknown

_1305360932.unknown



Actuality

Rating and risk

Regional systems


Laws

Data

Mathemetical tool



Data analysis


Conclusions

Conclusions


In work ordinal method of risk calculating, that was applied while investigation problem of depressiveness on base of statistical data about Ukrainian regions for a period of 2000-2006, is represented.

Risk of the whole system of Ukraine for 3 periods by criterion extra cost was calculated. Received results indicate of system risk increase on 10%.

Multicriterion approach for risk measurement was used for identification risk of industrial regions of the Kiev area.

Results show that criterion weight can influence upon output results. Risks of all regions and 2 cities of regional importance were calculated.

Conclusions


Results are important because efficiency of government stimulation of region development will be estimated by accuracy of "diagnosis" and adequacy of the using toolbox.

That is why so especial attention demands on estimation of development level of territories, adequate identification of depressive or problem-solving territories and determination of optimal influence mechanism upon situation.

QUESTIONS?


Risk Analysis Technology of Regional Systems on the Base of Statistical Rates

Documents

Transcript of Risk Analysis Technology of Regional Systems on the Base of Statistical Rates