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
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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.
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Rating and risk
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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.
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Regional systemsFinancial systemsPayment systems Banking systems Large corporations Regional systems
Information and Technology in the Knowledge Era
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.
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
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
System of risk calculation
Information and Technology in the Knowledge Era
Laws
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Mathematical models and optimization
Information and Technology in the Knowledge Era
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
Mathematical models and optimization
Information and Technology in the Knowledge Era
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
Mathematical models and optimization
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Data analysis
Information and Technology in the Knowledge Era
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
for period 2000 2005 years:
= 0.99755
for period 2000 2006 years:
= 1.05057
=3.29584
for period 2000 2004 years:
=0.29158
for period 2000 2005 years:
=0.30267
for period 2000 2006 years:
=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%.
Information and Technology in the Knowledge Era
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
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17
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19
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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
Information and Technology in the Knowledge Era
Pic.3 Regions risk in 2 period 2000-2005
Information and Technology in the Knowledge Era
Pic.4 Regions risk in 3 period 2000-2006
Information and Technology in the Knowledge Era
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Multicriterion approach for measurement of the strategic risk
Information and Technology in the Knowledge Era
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
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Criterion weights were equal:
.
_1305360937.unknown
Pic.6. Risk when and
Information and Technology in the Knowledge Era
Criterion weights were different: criterion weight of industrial product
, criterion weight of salary
.
_1305360934.unknown
_1305360935.unknown
Pic.7. Risk when and
Information and Technology in the Knowledge Era
Criterion weights were different: criterion weight of industrial product
, criterion weight of salary
.
_1305360931.unknown
_1305360932.unknown
Risk Analysis Technology Outline
Information and Technology in the Knowledge Era
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
Conclusions
Information and Technology in the Knowledge Era
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
Information and Technology in the Knowledge Era
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?
Information and Technology in the Knowledge Era