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I don't know if it applies to other countries, but in Canada practically all auto and home insurers routinely raise your insurance premiums after you make a claim, even for not-at-fault and purely accidental claims. I recently received a letter from my home insurer that proudly promised not to raise my premium after my first claim, as if it were an act of incredible generosity on their side.

If I understand correctly the mechanics of calculating premiums, they take into account the probability of insurable accidents and expected claim amounts. The probability is based on my age, income level, marital status, the location where I live, the frequency of accidents of various types in that location, etc.

The fact that I have a no-fault accident, e.g. my car's door gets dinged in a parking lot, or a tree branch breaks my house window, should not change the probability of future accidents or expected claim amounts. If that is true, how then they justify raising premiums (apart from "we want moar money")?

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    The fact that your car door gets ding may indicate that you car is parked frequently in a space or in a manner that it´s likely to get dinged. The fact that a tree branch breaks your windows may indicate there are more dead tree branches near your hose that no one looks after ... – Daniel Apr 17 '20 at 23:33
  • That's exactly why I am asking the question. The insurers seem to assume that insurable events are dependent, and the presence of one event increases the probability of future events, while in fact there is no reason for that. The branch that broke my window is no longer there, so the probability of another such event cannot be higher; it can only be lower or equal. – mustaccio Apr 17 '20 at 23:58
  • well the insurers have millions of datasets that seem to tell them otherwise, so really facts are on their side... – Daniel Apr 18 '20 at 0:00
  • Citation needed. – mustaccio Apr 18 '20 at 0:00
  • No fault does not mean unavoidable. – Kevin Aug 15 '20 at 23:32
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The probability of a claim is based on any and every factor they can use -- if statistics say that people who own dogs are more likely to make a claim, they'll consider adding a question about dog ownership to the insurance application.

By far the strongest indication that someone will make a claim in the future is that they've made a claim in the past. This covers all sorts of "hidden factors" that the insurance company can't account for with the other statistics they look at. For example, maybe there's something about how you park that makes it harder for others to judge where your car is, or maybe you've surrounded your house with eucalyptus trees.

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  • By far the strongest indication that someone will make a claim in the future is that they've made a claim in the past -- any source for that? Sounds counter-intuitive. Following this logic, when I buy insurance I have not made any claims yet, so the probability of me making a claim in the future is near 0. – mustaccio Mar 18 '20 at 22:00
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    @mustaccio No, they look at population averages given certain conditions. For example, for your initial policy they'll look at the accident rate for people of your age, locale, and maybe type of car to estimate the probability of your filing a claim. If you file a claim you move yourself into a different statistical category. You may be completely faultless in the accident, but the population of people who have been in accidents is enriched for accident prone drivers. They aren't judging you personally, just the statistical categories you belong to. – Charles E. Grant Mar 19 '20 at 1:25
  • @CharlesE.Grant, it also moves you into the category of "people who file claims". It costs more to insure the person who files a claim over a minor dent in the car door than it does to insure the one who just goes to the store for a $5 can of paint. – Mark Mar 19 '20 at 1:43
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    @mustaccio True, but not everybody has the same probability of being struck by lightning. The fact that a person was struck by lightning reveals information about them, namely, that it is more probable that they are in the group of people who are at higher risk of being struck. The same logic is at play with insurance premiums. Some people are more likely to file claims than others, but insurers don't initially know who is who. When people make claims, or go a long time without making claims, the insurer begins to find out. – Nobody Aug 16 '20 at 14:52
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    @mustaccio Of course, being struck by lightning doesn't actually change the odds you'll be struck by lightning again. It just allows humans to more accurately estimate what those odds are. Similarly, making an insurance claim doesn't make it more likely for you to make more claims in the future than you were already, but it allows the insurance company to recognize that you are higher risk than they thought you were in the first place. – Nuclear Hoagie Aug 17 '20 at 14:07
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At least here in the US there's also another factor at play: Many insurance companies offer claim-free discounts. Making a claim means you're no longer claim free. (Or there can be a middle ground--with my auto insurance if they recover every dollar they pay me then it's not counted as a claim. When an idiot didn't look and hit me I chose to fight it myself because they could easily end up in a position where something small wasn't worth the time and thus not recover every dollar. Clear-cut fault is irrelevant.)

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  • Thank you, "claim-free" discounts are indeed a thing, but in my view they indicate the same fallacy -- the fact that I didn't make any claims in the past X years does not indicate that I will not do so in the future; I might end up making an outrageously high claim next week, for reasons that may or may not be under my control. – mustaccio Aug 16 '20 at 19:19
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From your question and comments, I think you may be incorrectly reasoning about probability and specifically over-generalizing from the rule "occurrence of random events don't predict anything about future events".

Let's take a simple demonstration with dice, which hopefully shows how the insurer thinks about random events. Let's say we have 100 6-sided dice, and we've done everything we can to make sure they're all identical, short of actually rolling them. E.g., they all answered the same to various questions like age, income, etc.

We did a pretty good job, so let's say 99 of these dice are completely normal, fair dice, and one of them is bad and always rolls a 6. And we'll play a game where rolling a 6 is the same as having an insurable event and making a claim to the insurance company.

It's useful to think about what that "bad die" represents -- this is a person that looks the same as a normal person, but for whatever reason just makes a lot more claims. Maybe they're a jerk that lies about no-fault claims, maybe they keep parking their car under a rock-slide-prone area and can't be convinced otherwise.

Anyways, let's roll all the dice. As expected, of the 99 normal dies, around 16.5 should roll a 6, let's say exactly 16 do, and of course the bad die also rolls a 6. These dice all "make a claim" to the insurance company.

Now, what rates should we be charging to the 2 different groups: the 17 dice that rolled a 6 (we still don't know which one is the bad die), or the 73 dice that rolled something else? For the 73 dice that haven't filed a claim, the probability of filing a claim next time is still 1/6 = 16.7% as usual.

For the 17 that did file a claim, the expected number of claims on the next round is (1/6 * 16 + 1) / 17 = 21.5%. That difference in probability definitely matters to the insurance company who has millions of customers.

Overall, note that the probability of an individual die didn't change, and for a non-rigged die, nothing about the past rolls says anything about the future. That is, being struck by lightning didn't make anyone more likely to get struck by lightning in the second round. However, merely by filing a claim, you necessarily display externally-visible signals which are the same as people who are very expensive to insure (e.g., those who file a lot of claims), so to the insurer, it makes sense to lump you in with everyone who filed a claim.

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  • Thanks, that's a good explanation, except for the fact that in this example the insurer can't know that there is a "bad" die -- it might as well be in the other group. Therefore, they can't arrive at your 21.5% without having outside knowledge -- for all they know, in the second round the dice throwing 6 will be all different from those of the 1st round. Are you saying that their (insurers') approach is to assume that they consider any die that rolls 6 to accumulate in the "bad" group? Leading to eventually every die to end up in that group? – mustaccio Aug 16 '20 at 19:07
  • The "bad die" is a simplification to make the math easy. In reality, there's a "distribution" of people in the population, probably shaped like a bell-curve. Some people in the population are more likely to file claims and some are less likely. It is definitely true that exactly half are more likely to file claims than the median person. After, say, a year, people from the bad half are more likely to have filed a claim, but not guaranteed. But still, on average, the population that filed claims contain more people from the upper end of the bell curve than the lower end. – letterX Aug 16 '20 at 19:17
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    And yes, everyone does eventually end up in the "has filed at least one claim" group, just like we'd expect in real life. But by the time that's happened, the really bad apples have ended up in the "filed at least 2 claims", 3 claims, 4 claims, etc. and are getting charged even more. For people that take a long time to file their first claim, the insurance company graciously gives you a "discount" of "first no-fault claim won't increase your premium", because they've demonstrated over time that they're in the less likely to file population. – letterX Aug 16 '20 at 19:19

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