[jbeam]

Very interesting article that cuts to the core of many of the issues with pricing insurance products. While the phrase is hardly limited to the actuarial world, "all models are wrong, but some are useful" is definitely an extension of this.

The fluid nature of probability is the center of the insurance universe. Probability is always a moving target in the insurance world. Indeed, if it weren't, there wouldn't be much of a need for actuaries. Much of actuarial training revolves around the idea of credibility -- how credible is your sample set, what alterations should you make to old data to make it relevant to today, and what data should you add to it as a complement in order to relieve the model of the biases inherent in your sample size. This is inherently Bayesian in it's approach.

Where it truly gets interesting is that insurance companies are very cognizant of tail risk -- the 1-in-100, 1-in-250, 1-in-500 events that can cause insurer insolvency if not properly accounted for. You can survive a miscalculated loss trend within reasonable bounds, but if you haven't thought about the potential Cat 5 hurricane that hits Miami-Dade then you are going to have some very unhappy investors. When it comes to these types of events, you mostly need to be in the right ballpark. The order of magnitude matters more than the exact number -- albeit the exact number matters quite a bit for regulatory reasons. This type of calculation for property lines has largely been outsourced to the stochastic models developed by companies such as AIR and RMS. A sudden change in their models, which I think is likely after this record breaking hurricane season, can inflict capital pressure on the industry almost instantly.[1]

There are some actuarial papers from around 50 years ago that discuss information entropy as another way to approach the issue of constructing probability models, but they never really caught on. It seems that is likely due to the lack of widespread computing power. I'm hoping these ideas can gain some steam now that we can construct some of these distributions from Python and R.

[1] There is a fantastic article by Michael Lewis that describes this issue at great detail: https://www.nytimes.com/2007/08/26/magazine/26neworleans-t.h...

[sxzxs]

For me, it comes down to what kinds of these risky models are most interesting. Some can be interesting because of potential profit or minimizing loss (financial or actuarial) and others are inherently (theoretical physics).

To add to your tail risk point - I wonder how many people foresaw the Venezuelan oil crisis way back when, or even less likely, the Saudi Arabian oil complex attack in 2019. And of course, the current situation we're in with CoVID that an entire university of forward thoughtful looking people didn't call until it was a week away. As an aside, do insurance companies significantly alter their policies when such a cat-5 hurricane is imminent? What preparations would they make in the face of that sort of event?

Are you talking about chaos theory in the last paragraph? I'll read that article you linked in a bit and see what more I have to say, from skimming through it looks as though my question from the previous paragraph may be answered.

[jbeam]

>as an aside, do insurance companies significantly alter their policies when such a cat-5 hurricane is imminent? What preparations would they make in the face of that sort of event?

You cannot retroactively alter a policy, for obviously good reasons. The main preparation policy-wise is that insurance companies do not knowingly write new policies in the affected area when disaster is ongoing or imminent. Reinsurers will also avoid writing new treaties (which is what a standard reinsurance policy is called) -- for these reasons the Florida cat reinsurance market is typically dominated by policies that incept on June 1st and run to May 31st of the next year.

Internally, the companies will start modeling what they think their potential losses will be almost immediately, as investors expect a fairly quick turnaround on getting initial loss estimates out the door.

There's a fairly new paper here, albeit not yet peer reviewed, on the promise of maximum entropy models in an actuarial setting. The appendix has references to the earlier papers: https://www.casact.org/pubs/forum/20wforum/07_Evans.pdf

[alisonkisk]

> You cannot retroactively alter a policy,

Sure you can. Insurers refuse claims all the time. You just claim that the assumptions of the policy were not met. Since assumptions are always idealizations of the messy real world, such a claim is *always" true

[sxzxs]

Thanks for the link, I'll check it out.