# Extreme Events

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```					Extreme Events

John Kollar, ISO May 19, 2003

Estimated Insured Losses (9/11/01)
 \$25-45 billion  18-24 billion of Property (including B.I.)  1-2 billion of Workers Compensation  3-10 billion of General Liability  2-5 billion of Aviation  1-3 billion of all other

Extreme Events
 Unexpected  Unusually large  Sudden  Large (insured) losses  Multi-line (clash losses)  Extreme Event Theory (Tom)  AAA Extreme Event Risk Committee
 Terrorism focus

 Non-terrorism (cyber risk, Northeast hurricane, Tokyo

earthquake)

Underwriting Risk Considerations
 Quantify the underwriting risk (needed capital), taking

into account:
 Loss volatility  Correlation between lines (dependencies)  Adverse loss development for long-tailed lines

Loss Volatility Requires More Capital

Insurer A

Insurer B

}

Less Capital

}

More Capital

Expected costs

The Effect of Correlation
Capital
Low Correlation

Capital

High Correlation

Insurer A

Insurer B

Low Risk

High Risk

Total

Low Risk

High Risk

Total

Short vs Long-Tailed Lines
Short-Tailed Lines Release most capital at the end of 1st year. Long-Tailed Lines Release a portion of capital at the end of each year.

Year 1 Year 2 Year 3 Year 4

Y1

Y2

Y3

Y4

Extreme Event Analysis
 Analyzed 19 insurers individually.
 Calculated aggregate loss distributions using

information by annual statement lines of business  By insurer  Total for the “industry” of 19 insurers  Net of reinsurance
 Used exposure reported to ISO as input into AIR’s

CLASIC/2 catastrophe model for hurricanes and earthquakes
 Generated 10,000 years for hurricane, earthquake

and all other losses.  Correlations between lines and insurers are driven by uncertainty in claim frequencies and claim severities.
 Compare the losses for each of the 10,000 years to

insurer capital.

Count
100 200 300 400 600 700 800 900 0
1 2 G ro up ro up G

500 442

197

G ro up 3

616

G ro up 4

17

G ro up 5

28

G ro up 6 7 ro up G

534

129

G ro up 8

3

G ro up 9 G

62

ro up 10 11 12 13 ro up 14 ro up ro up ro up

189

G G G G G G G G G

310

65 367 119

ro up ro up ro up ro up ro up

15 16 17 18 19

Number of Times Exceeded 25% of Surplus

27 32 351 773 289

Count
10 15 20 25 30 35 40 0
1

5

G ro up

5

G ro up 2

0

G ro up 3

18

G ro up 4

5

G ro up 5

0

G ro up 6 7

22

G ro up

5

G ro up 8

0

G ro up 9 G

0
10 11

ro up ro up ro up 12

17

G G G ro up 13 ro up G G G G G ro up ro up ro up ro up ro up G

8

0 7
14

0
15

0
16

0
17

Number of Times Exceeded 50% of Surplus

4

18 19

35

1

Count
G
10 12 0 2 4 6 8

ro up 1

0

G ro up 2

0

G ro up 3

0

G ro up 4

0

G ro up 5

0

G ro up 6

0

G ro up 7

0

G ro up 8

0

G ro up 9 G

0
10 11

ro up ro up

11

G G

0
12

ro up

G ro up 13 ro up G G G G G ro up ro up ro up ro up ro up G

0 0
14

0
15

Number of Times Exceeded Surplus

0
16

0
17

0
18

0
19

0

Integrated Catastrophe & Non-Catastrophe Losses

0.75

Normalized Deviation...

0.50 Normal Hurricane Earthquake

0.25

0.00

-0.25 1 3 5 7 9 11 13 15 17 19 Insurer #

Extreme Events = Worst 500 Years
 “Industry” defined as sum of the 19 insurers.

 Selected the worst (highest losses) 500 (5%)

“industry” years.
 Graphs on spreadsheet show results.  Results show that catastrophes drove losses for 8

of the worst years (net of reinsurance).
 However most of the top 500 did not involve

catastrophes (net of reinsurance).

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Lingjuan Ma MS