Black Swan Theory: We know absolutely nothing & the finding of atypical events

optimization-method

Carlos Castro Correa AXA Mxico

Black Swan Theory

2

3

Unexpected Events

America Discovery

4

Unexpected Events

5

Non-experienced based ocurrence

Unexpected Events

6

All available information is useless

Non-experienced based ocurrence

Unexpected Events

7

All available information is useless

Inability to forecast

Non-experienced based ocurrence

Unexpected Events

8

9

Impossible Occurrence

10

Black Swan Event

11

Black Swan features

Retrospective Explanation

12

Retrospective Explanation

13

Black Swan features

Retrospective Explanation

Extreme Impact

14

Extreme Impact

15

Black Swan features

Retrospective Explanation

Extreme Impact

Unexpected or not Probabable

16

Unexpected or not Probabable

Forecasting Techniques

17

Forecasting Techniques

Gaussian Assumption

18

9/11 Attacks

19

Financial Crisis

20

21

Physical Variables

Height

22

Social Variables

Stock Price

23

Experience is not enough

24

Turkey Paradox

25

Restrictions and Opportunities

Negative empiricism Black Swan.

Consciousness of the existence of

black swan.

Adequate use of statistical tools.

26

Black Swans Atypical

K

S

I

R

T N E

M E G A N A

M

27

Atypical Events

28

Atypical in Risk Management

Negative Impact

Not Expected

29

Catastrophic Hurricane

30

Atypical Event?

Establish an fair limit to distinguish past black swan events

Segmentation between Typical & Atypical Events

31

Experienced based limits

Fixed Amont $

Fixed Percentile 5%

The last n events

32

Atypical Event

Given a distribution, the data does not belong to the behavior of the distribution.

33

Atypical events optimization-

method

34

Data Set

X original data set amount associated

35

First Step

m subsets Si Percentile Pi

36

First Step

Si C Sj if i < j

m subsets Si Percentile Pi

37

First Step

Si C Sj if i < j

lSjl = k

m subsets Si Percentile Pi

38

Establish a meausure

Goodness of fit test

39

Establish a meausure

Goodness of fit test

Kolmogorov-Smirnov

40

Family F

l F l = n

f()

Parameter

41

Adjustment level

S

42

Better adjustment

S SSS

43

Better adjustment

S SSS

S

Best adjustment for every subset

*

44

Optimization Problem

* SS

45

Best Adjustment

=

S S*

S

46

Best Adjustment

Percentile AmountHYDRO 0.95 863'071 FIRE 0.93 237'888 MISC 0.98 129'507 RC 0.89 79'448 TEC 0.96 148'088 EQ 0.83 480'000

TRANSPORT 0.98 709'488

47

Weakness of the method

48

Size Penalization - Percentile

S =

S * Per 2

S

Per 20 1

49

Risk Management Applications

50

Data Set

51

Typical Data

52

Solvency

Best Estimate Liabilities

99.5 Percentile

53

Economic Capital

Best Estimate Liabilities

99.5 Percentile

Solvency Capital

54

Atypical Data

55

Atypical Data

Reinsurance Policy

56

Applications in RM

Claim Control Strategies

Reinsurance Policy

Economic Capital Modeling

57

Mixture of distributions

58

Mixture of distributions

59

Mixture of distributions

60

Mixture of distributions

61

Conclusions

Black Swan Theory: We know absolutely nothing & the finding of atypical events optimization-method Black Swan TheorySlide Number 3America DiscoverySlide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Black Swan EventSlide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Forecasting TechniquesForecasting Techniques9/11 AttacksFinancial CrisisPhysical VariablesSocial VariablesExperience is not enoughTurkey ParadoxRestrictions and OpportunitiesBlack Swans AtypicalSlide Number 27Atypical in Risk ManagementCatastrophic HurricaneAtypical Event?Experienced based limitsAtypical EventSlide Number 33Data SetFirst StepFirst StepFirst StepEstablish a meausureEstablish a meausureFamily FAdjustment levelBetter adjustmentBetter adjustmentOptimization ProblemBest AdjustmentBest AdjustmentWeakness of the methodSize Penalization - PercentileSlide Number 49Data SetTypical DataSolvencyEconomic CapitalAtypical DataAtypical DataApplications in RMMixture of distributionsMixture of distributionsMixture of distributionsMixture of distributionsSlide Number 61Slide Number 62