Transcript Topic 4. Quantitative Methods

4. Quantitative Methods &
Applications
BUS 200
Introduction to Risk Management and Insurance
Fall 2008
Jin Park
Overview
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Probability Distribution
Application in Risk Management &
Insurance
Insurance Premium
Using Probabilistic Approach
Probability Distribution
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Representations of
all possible events
along with their
associated
probabilities
Example;
Total number of points
rolled with a pair of
dice.
Outcome
Probability
2
1/36
3
2/36
4
3/36
5
4/36
6
5/36
7
6/36
8
5/36
9
4/36
10
3/36
11
2/36
12
1/36
Different Events
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Mutually exclusive (events)
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The probability of two mutually exclusive
events occurring at the same time is
____ .
Collectively exhaustive (events)
Independent (events)
Probability Distribution
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Measure of central tendency
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Mean, Median, Mode
Measure of variability (risk)
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Difference (Min, Max)
Variance
Standard deviation
Coefficient of variation
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“Unitless” measure
Probability Distribution
B
A
A
B
Mean A, B
Mean A
Mean B
Exercise 1
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Article: Mom wins dream house
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Number of tickets
Chances of winning
Price of a ticket
Total proceeds
Total payouts
Exercise 2
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Article: Cadillac Escalade tops with
car thieves.
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Severity per insured Escalade
Theft frequency
Severity per theft
Insurance Premium
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Gross premium
= Pure premium + Risk charge + Other loadings
 Pure premium = Expected Loss (EL)
= Expected Frequency x Expected Severity
 Estimated amount to pay for expected loss.
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Risk charge (Risk loading)
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Amount to cover the risk that actual loss may be
higher than expected loss
Other Loadings
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Expenses and profits
Risk Charge (Risk Loading)
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What determines the size/magnitude of the
risk charge?
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Amount of available past information to estimate
EL
The level of confidence in the estimated EL.
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The higher the level of confidence in the estimated EL,
the _____ the risk charge.
The number of loss exposures insured by the
insurer
The size of loss exposures
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Risk charge for terrorism coverage would be _______
than that for personal automobile insurance.
Probabilistic Risk Analysis
Simple example of event tree
Early
Detection
Sprinklers
Work?
Fire stop Probability
OK?
No
(.01)
Yes
(.999)
No
(.10)
Yes
(.99)
Fire
No
(.001)
Yes
(.90)
What is the expected severity of a fire?
10-6
Loss
$100 mil
.000999 $10 mil
.099
$100 K
.90
0
$19,990
Probabilistic Risk Analysis
What if there is no sprinkler system…
Early
Detection
Fire stop Probability
OK?
Loss
No
(.001)
10-4
$100 mil
Yes
(.999)
.0999
$10 mil
No
(.10)
Fire
Yes
(.90)
What is the expected severity of a fire?
.90
$1,009,000
0