Post on 02-Nov-2015
description
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
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Atypical in Risk Management
Negative Impact
Not Expected
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Catastrophic Hurricane
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Atypical Event?
Establish an fair limit to distinguish past black swan events
Segmentation between Typical & Atypical Events
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Experienced based limits
Fixed Amont $
Fixed Percentile 5%
The last n events
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Atypical Event
Given a distribution, the data does not belong to the behavior of the distribution.
33
Atypical events optimization-
method
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Data Set
X original data set amount associated
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First Step
m subsets Si Percentile Pi
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First Step
Si C Sj if i < j
m subsets Si Percentile Pi
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First Step
Si C Sj if i < j
lSjl = k
m subsets Si Percentile Pi
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Establish a meausure
Goodness of fit test
39
Establish a meausure
Goodness of fit test
Kolmogorov-Smirnov
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Family F
l F l = n
f()
Parameter
41
Adjustment level
S
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Better adjustment
S SSS
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Better adjustment
S SSS
S
Best adjustment for every subset
*
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Optimization Problem
* SS
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Best Adjustment
=
S S*
S
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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
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Weakness of the method
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Size Penalization - Percentile
S =
S * Per 2
S
Per 20 1
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Risk Management Applications
50
Data Set
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Typical Data
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Solvency
Best Estimate Liabilities
99.5 Percentile
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Economic Capital
Best Estimate Liabilities
99.5 Percentile
Solvency Capital
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Atypical Data
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Atypical Data
Reinsurance Policy
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Applications in RM
Claim Control Strategies
Reinsurance Policy
Economic Capital Modeling
57
Mixture of distributions
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Mixture of distributions
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Mixture of distributions
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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