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  #1  
Old 08-28-2019, 07:20 PM
ActuaryInWoods ActuaryInWoods is offline
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Default Uncertainties around hurricane models

If we run or apply a particular historical hurricane event (like Hurricane Irma, known hurricane category, landfall locations, sustained wind speed, sustained pressures, and other characteristics models typically relied on) to company's historical exposures (assuming decent quality exposure data, size of book is large enough) in-force as of August 30, 2017, just before landfalls, what degree of off you would reasonably expect between model results and actual company's claim costs?

I am talking about historical events, means primary uncertainties associated with hazard are almost gone. Lets take Hurricane Irma for example, the sustained wind speed, pressure, amount of rainfalls are known at a particular location. So main uncertainties left here is the secondary uncertainty associated with vulnerability.

if modeled results for a particular historical event are 50% more or less than the actual, would that be reasonable?

If modeled results for a particular historical event are 50% more or less than the actual and this degree of error is reasonable, the model estimates of a hurricane event immediately following a landfall could be more off than 50% and we really cant rely on that for funding purpose.

Last edited by ActuaryInWoods; 08-30-2019 at 05:45 PM..
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Old 08-30-2019, 11:24 AM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
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It all depends. Suppose that you only insured two houses ($100K each) in the area where the storm cam ashore and that your model predicted 5% loss (above the deductible) for each house. Now here are a few things that might happen:

1) hurricanes spawn tornadoes. Tornado destroys one house completely.

2) both houses get lucky and suffer damage below their deductibles.

3) something in between 1 and 2

On average, you'll have $10,000 of loss but it could easily range from 0 to 100,000 --- this is assuming that your model is perfect.

Of course, with more risks you would expect results closer to the average because of the Law of Large Numbers.

Upshot: Since you could easily observe results far away from the mean even when your model is correct, it will be very hard to use actual results to determine if the model is correct or not.

("Correct" meaning useful --- all models are wrong.)
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Old 08-30-2019, 11:34 AM
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But remember that you want to apply the model to your current exposures, not to your historic exposures. That was the huge mistake pre-Andrew that led to modern hurricane modelling.
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Old 08-30-2019, 12:32 PM
magillaG magillaG is online now
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Remember that hurricane models are an improvement over traditional actuarial methods, which aren't very good at dealing with the huge process variance in hurricane losses. Even an error on the order of 100% is a large improvement in that sense. For example, think about applying traditional methods to a history with 3 storms, which has an error of at least 50% from only the frequency.

Also, the error on the average loss across an entire year will be different from the loss of the predicted error from a single storm. The former has additional uncertainty due to frequency. However, the latter will depend on correctly modeling the effects of a single storm, and these errors might average out over all the possible storms that can occur in a year.

Another way to estimate the error is to compare several different reliable models. Their range is another estimate of the (minimum) error.
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Old 08-30-2019, 01:00 PM
ActuaryInWoods ActuaryInWoods is offline
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We are talking about historical events, means primary uncertainties associated with hazard are almost gone. Lets take Hurricane Irma for example, the sustained wind speed, pressure, amount of rainfalls are known at a particular location. So main uncertainties left here is the secondary uncertainty associated with vulnerability. The three scenarios you provided seem associated with primary uncertainty.


Quote:
Originally Posted by Colymbosathon ecplecticos View Post
It all depends. Suppose that you only insured two houses ($100K each) in the area where the storm cam ashore and that your model predicted 5% loss (above the deductible) for each house. Now here are a few things that might happen:

1) hurricanes spawn tornadoes. Tornado destroys one house completely.

2) both houses get lucky and suffer damage below their deductibles.

3) something in between 1 and 2

On average, you'll have $10,000 of loss but it could easily range from 0 to 100,000 --- this is assuming that your model is perfect.

Of course, with more risks you would expect results closer to the average because of the Law of Large Numbers.

Upshot: Since you could easily observe results far away from the mean even when your model is correct, it will be very hard to use actual results to determine if the model is correct or not.

("Correct" meaning useful --- all models are wrong.)

Last edited by ActuaryInWoods; 08-30-2019 at 01:18 PM..
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Old 08-30-2019, 01:11 PM
ActuaryInWoods ActuaryInWoods is offline
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I am asking about error resulting from a single historical storm with all known characteristics. Mainly the error range associated with vulnerability. I made clarifications to original posting.

Quote:
Originally Posted by magillaG View Post
Remember that hurricane models are an improvement over traditional actuarial methods, which aren't very good at dealing with the huge process variance in hurricane losses. Even an error on the order of 100% is a large improvement in that sense. For example, think about applying traditional methods to a history with 3 storms, which has an error of at least 50% from only the frequency.

Also, the error on the average loss across an entire year will be different from the loss of the predicted error from a single storm. The former has additional uncertainty due to frequency. However, the latter will depend on correctly modeling the effects of a single storm, and these errors might average out over all the possible storms that can occur in a year.

Another way to estimate the error is to compare several different reliable models. Their range is another estimate of the (minimum) error.

Last edited by ActuaryInWoods; 08-30-2019 at 01:19 PM..
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Old 08-30-2019, 02:10 PM
magillaG magillaG is online now
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Quote:
Originally Posted by ActuaryInWoods View Post
I am asking about error resulting from a single historical storm with all known characteristics. Mainly the error range associated with vulnerability. I made clarifications to original posting.
If you are getting 50% from historical storms, then that strikes me as not an reasonable estimate (if it is that large, then the real uncertainty will be asymmetric of course) but I would check what multiple models give for the same exposure.

I believe the results for individual storms can really depend on correctly modeling the path of the storm, and also the associated wind speeds, which seems to be very difficult. I think Irma may have been an especially difficult one, because it was so large that it had strange behavior. The models may have to try to make the storms "fit" into their parametric wind models, as opposed to using the actual measured wind speeds. Also the models can only guess at aspects of the claims environment after, like demand surge, litigation, etc.

I'm assuming too that you have enough policies that the process variance of the single storm, i.e. what CE described below, will not matter.
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Old 08-30-2019, 02:48 PM
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Are you controlling for size of book, "average" exposure for a given location, and changes in required building codes between the modeled exposures and the historical exposures?
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Old 08-30-2019, 03:52 PM
ActuaryInWoods ActuaryInWoods is offline
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Quote:
Originally Posted by Vorian Atreides View Post
Are you controlling for size of book, "average" exposure for a given location, and changes in required building codes between the modeled exposures and the historical exposures?
Yes. Size of book is stable. Building code change is not a concern.
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Old 08-30-2019, 04:05 PM
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And is there a material difference in the distribution of the exposures between the two?

For example, has your book "migrated" toward the coast?

Also, while the "average" exposure might still be stable, the "migration" toward the coast might actually place more (current) exposure to loss due to an event than historical.
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