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  #1  
Old 04-01-2019, 02:03 PM
jackandrew jackandrew is offline
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Default Frequency GLM ~ Claims without exposure?

Hi there,

New to GLM pricing with auto insurance. I'm wondering if following issue comes up for anybody in auto pricing - your frequency model is a Poisson (log link) with:

ClaimCount ~ Variables +offset(log(Exposure))

Your data is at the driver/vehicle level, so your exposure for one car year could be split up among all the drivers on that policy for that year (so, if one car and two drivers for one year, you have 0.5 exposure for each driver). This seems nice to have driver level variables lined up with claims.

A fraction of claims come from undisclsoed/uninsured drivers. So, the claim counts/losses are associated with the unknown driver, not necessarily the insured driver. Hence, the uninsured driver gets their own row in the data. The complication is that the undisclosed driver has 0 exposure, which obviously doesn't fly in the above Poisson GLM with exposure as an offset.

What is the standard approach to data rows where we have claims > 0 but exposure = 0? Do we usually only model at vehicle level (i.e. take minimum driver age, or "worst" performing gender for driver level variables etc...) or do we filter out uninsured drivers and make some kind of adjustment to the model? Or something else?
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Old 04-01-2019, 02:12 PM
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Vorian Atreides Vorian Atreides is offline
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Think about how the GLM is going to be used. Do you think Underwriting is going to ask "what sort of uninsured drivers are going to hit you?" as a way to determine the premium to charge?

Spoiler:
Bottom line, if you're building a pricing GLM, you need to have predictor variables associated with the exposure that you're going to be rating.


Also, are the claims associated with a specific driver? Is there a reason that you're assuming equal exposure for each listed/available driver? How likely are you going to bias your results by having 1 claim associated with a (high-risk) driver using the vehicle only 10% of the time vs. having 1 claim with the same vehicle with the (other, lower risk) driver using the vehicle 90% of the time?

Finally, are you modelling all losses (BI liability, PD liability, 1st party coverage, etc.) together?
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Old 04-01-2019, 02:47 PM
jackandrew jackandrew is offline
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Thanks for your response.

The claims are by driver, which is why this question emerges in the first place. The equal division of exposure among insured drivers is a starting point, I will address its reasonableness eventually (it certainly affects any kind of loss ratio analysis with driver level variables, so I will have to address it). I am creating separate models for each coverage, and am starting out by modeling freq/sev instead of loss cost, but will evaluate that strategy by coverage when I get there.
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Old 04-01-2019, 11:08 PM
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Tacoactuary Tacoactuary is offline
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You can consider household averaging. (https://www.casact.org/education/ann...uts/gannon.pdf)
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Old 04-02-2019, 08:31 AM
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An alternative is to create an ensemble model where you create a series of models that assume 100% exposure for one driver associated with the vehicle--so, for example, create n models where n = max drivers for 1 vehicle. Then look to average results across runs for various characteristics.


Another alternative, is to use "driver years" as your exposure and assume that 100% of the car year is associated with each driver.
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Old 04-02-2019, 12:49 PM
MoralHazard MoralHazard is offline
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Why not build two models? One to predict claims frequency for the known drivers, which is modeled at the vehicle/driver level. The second model separately predicts frequency of claims pertaining to undisclosed drivers, and that is modeled at the vehicle level only. The total vehicle expected claims is the sum of all known driver E[claims] + the unknown driver E[claims].

If you need the pricing to be on a "per driver" basis, then where to slot the undisclosed driver premium just becomes a post-hoc allocation issue, but shouldn't affect the modeling decisions.
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Old 04-02-2019, 01:09 PM
jackandrew jackandrew is offline
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Quote:
Originally Posted by MoralHazard View Post
Why not build two models? One to predict claims frequency for the known drivers, which is modeled at the vehicle/driver level. The second model separately predicts frequency of claims pertaining to undisclosed drivers, and that is modeled at the vehicle level only. The total vehicle expected claims is the sum of all known driver E[claims] + the unknown driver E[claims].

If you need the pricing to be on a "per driver" basis, then where to slot the undisclosed driver premium just becomes a post-hoc allocation issue, but shouldn't affect the modeling decisions.
Thanks for your suggestion - this was the direction I was planning on going if there is not a standard approach to this issue. From the responses so far it sounds like there's a few ways to go about it. But picking out variables that are particularly predictive for undisclosed driver claims seems very natural to me.
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Old 04-02-2019, 03:13 PM
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Quote:
Originally Posted by jackandrew View Post
Thanks for your suggestion - this was the direction I was planning on going if there is not a standard approach to this issue. From the responses so far it sounds like there's a few ways to go about it. But picking out variables that are particularly predictive for undisclosed driver claims seems very natural to me.
Keep in mind that "predictive modeling" is actually a lot more proprietary than "standard" processes.

The underlying actuarial principles should still be satisfied, but the actual modeling process can be pretty flexible to attend to whatever situation you need to address. The real key is adequate documentation that another actuary could follow.
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