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#1
01-06-2004, 03:28 PM
 ET MAN Member Join Date: May 2003 Location: Dallas, Texas Posts: 259
reinsurance question

Does anyone know what a formal definition of expected loss would be?

thanks,
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#2
01-06-2004, 06:14 PM
 Jables Wonderboy CAS Join Date: Jan 2003 Location: AO Retirement Home Studying for kitchen utensilry degree College: Crazy Go Nuts University Favorite beer: Sam Adams, Dos Equis, Arrogant Hagbard, Clydesdale Juice Posts: 33,769
Re: reinsurance question

Quote:
 Originally Posted by ET MAN Does anyone know what a formal definition of expected loss would be? thanks,
Playing poker against Bama?
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#3
01-06-2004, 06:15 PM
 BassFreq Member CAS Join Date: Jun 2003 Location: Chicago Studying for all eternity Favorite beer: Duff Posts: 1,213

According to my insurance dictionary, an expected loss is "probability of loss upon which a basic premium rate is calculated."

Of course, that's a formal definition for insurance, for reinsurance it probably means something completely different, like the expected value of ultimate losses.
#4
01-07-2004, 08:08 AM
 joeorez Member Join Date: Oct 2002 Location: New York Posts: 730
OK, I'll bite:

Let x be a continuous random variable denoting loss, defined on 0 &lt;= x &lt;= b, where b is possibly infinite, having probability density function f(x).

Then the expected loss equals INTEGRAL FROM 0 TO b OF [ xf(x)dx ].

If you are looking for a definition under some more restrictive circumstances (such as "How are expected losses defined for the NCCI experience plan?"), then please let us know.
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#5
01-07-2004, 10:28 AM
 ET MAN Member Join Date: May 2003 Location: Dallas, Texas Posts: 259
thanks

I work at a Reinsurance Company and I am trying to determine how the Expected Loss is calculated.

Accordingly they provided data points..

Estimated Loss, Estimated Annual Probability of Exceedance,

I could derive the probability of attachment and the probability of exhaustion but when it came to Expected Loss. I am clueless..

Est Loss Est Prob
1 0.5
2 1.0
3 1.5
4 2.0

Attachment point = 1.0
Probability of Exhuastion = 0.5
Expected Loss = ??

thanks
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Sometimes you can get what you want and still not be very happy.
#6
01-07-2004, 01:38 PM
 Modeler Member Join Date: Sep 2003 Posts: 346
Re: thanks

Quote:
 Originally Posted by ET MAN I work at a Reinsurance Company and I am trying to determine how the Expected Loss is calculated. Accordingly they provided data points.. Estimated Loss, Estimated Annual Probability of Exceedance, I could derive the probability of attachment and the probability of exhaustion but when it came to Expected Loss. I am clueless.. Est Loss Est Prob 1 0.5 2 1.0 3 1.5 4 2.0 Attachment point = 1.0 Probability of Exhuastion = 0.5 Expected Loss = ?? thanks
These numbers make no sense. What am I missing? How can a probability be > 1 ??
Probability densities can be, but those only come from continuous distributions and that's not what you're showing here.

Of course I don't recall what "attachment point" means either, so maybe I haven't studied the right material for whatever this is.
#7
01-07-2004, 03:29 PM
 BassFreq Member CAS Join Date: Jun 2003 Location: Chicago Studying for all eternity Favorite beer: Duff Posts: 1,213

I don't know about "Probability of Exhuastion" (Probability of Exhaustion for me is high since I'm quite out of shape from studying when I should be exercising), but I would calc expected loss as

E[Loss] = Sum [ Est Prob<sub>i</sub> * (Est Loss<sub>i</sub> - Attchmnt ) ]

.
#8
01-07-2004, 04:39 PM
 ET MAN Member Join Date: May 2003 Location: Dallas, Texas Posts: 259
clarification

TO: Bass Freq,

Exactly what I was looking for.

to Modeler.. I should've noted that 1.0 and 1.5 etc are percentages.. so 1=1%..

thanks
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#9
01-12-2004, 10:50 PM
 Skippy Member Join Date: Sep 2001 Posts: 83
Re: thanks

I think this is more complicated than you and others are lead to believe.
You mention that you have loss and estimated "annual probability of exceedence".

Generally this type of output comes from a standard catastrophe model such as RMS.

You're sample table is obviously made up and is not possible - probability of loss exceeding 1 = 0.5%, probability of loss exceeding 2 = 1.0%. Both of these cannot be true since if a loss exceeds 2 it must also exceed 1...

Getting back to the expected loss, if this is output from an RMS model (or similar), get the event list output instead of the probability of exceedence curve. The event list gives you a listing of all possible losses (as far as the model is concerned) and their annual frequency. It is then a simple matter of multiplying the loss (or loss less the attachment, if this is what you're after) by the frequency and then summing these up.

If you don't have the event listing you can probably estimate the expected loss by taking the difference between successive loss probabilities as the frequency of a loss equal to the mid-point between the two losses. eg

Loss prob of exceedence
1M 0.5%
2M 0.4%
3M 0.3%
4M 0.2%
5M 0.1%
6M 0.001%

This can be transformed into:
Loss estimated frequency
1.5M 0.1%
2.5M 0.1%
3.5M 0.1%
4.5M 0.1%
5.5M 0.099%
6M 0.001% (need to take a guess at this loss size, but if prob is small enough it doesn't matter much)

and then this distribution can be used to estimate the expected loss.

This only really works if you are only looking at extreme events with lowish probabilities involved (and very low prob of more than one loss).

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