A New Perspective on Actuarial Science

[AndrewLouca]

Originally Posted by DamSon

These are good questions. I would also ask what the benefit of this notation is over other existing structures.

While the idea of creating standardized notation is great, there needs to be a push from the top down rather than bottom up. Consistent notation on exams as well as journals like Variance should be the starting point. Putting together another one off on notation is nice and all, but like others mentioned it's about the take up rate.

I'm not at the top, so I can't push from there. Also, a consistent notation is going to have to re-do all past results in that notation. Honest question: is a journal like Variance the place for something like that?

Originally Posted by DamSon

I also looked through your text and I'm not quite sure what exactly it's supposed to be.

Thanks for looking through it

This is just the first part of the text, and it's supposed to mathematically explain why insurance is necessary, and once that's established, then talk about more traditional insurance and actuarial related topics.

Originally Posted by DamSon

You mention a focus on notation, but there's a lack of explanation or buildup of some of your notation itself. The binomial distribution is an example, you don't really explain it and just start using that notation and it's explained later in Chapter 4, but the references to it start in Chapter 3.

Can you point me to the binomial example? The first time I mention the binomial distribution is in chapter 3, on page 17. I say

Since L^G is the sum of two independent Bernoulli random variables, it is a binomial random variable.
L^B ~ 50,000Bin(2,0.002)

I thought Bin(N,p) was standard for representing a binomial distribution, but maybe not. I'm going to assume knowledge or probability as a prereq for the book. I want the text clear, so if anyone has constructive criticism, I welcome it. The text isn't set in stone, I want to make it better where I can. Also, maybe I am just misunderstanding what you mean.

Originally Posted by DamSon

Was there any plan to work with the CAS on this or are you just soliciting feedback on your text?

I emailed someone at CAS asking for some advice, but no response yet. I also looked at their site for submitting publications (https://www.casact.org/pubs/index.cfm?fa=submission)

As far as I can tell, my work would fall under the Monograph guidelines. But as I read more about the process, I discovered that one of their requirements was that CAS gets the exclusive right, title, and interest to the paper, including the right of the CAS to edit the paper and publish the author's name in connection with the publication of the monograph.

This is not something I'm comfortable with at the moment.

Originally Posted by DamSon

My personal opinion on this is that life insurance notation is messy and we shouldn't move towards that type of notation. I'd prefer not having to draw a line under something, add a subscript and superscript alongside a hat just so it's "consistent".

If you had to design a notation, what kind of things would you want to include?

Originally Posted by DamSon

You mentioned that notation can add value and lead to interesting results, and I agree somewhat but I think that comes from a simplification of notation rather than increasing the complexity.

I agree, increasing complexity just for the sake of complexity is dumb. That's not what I want to do, and I don't think I am. But, oversimplification isn't good either. Albert Einstein has a related quote that I like a lot.

Everything should be made as simple as possible, but no simpler. - Albert Einstein

[nonactuarialactuary]

Originally Posted by AndrewLouca

Can I ask why superscripts as identifiers should be illegal?

Because they’re annoying to type with standard tools. Try typing R2 on Actuarial Outpost with the “2” properly formatted as a superscript. I don’t think you can do it unless you bring out the LaTeX formatting, and let’s be honest, nobody has time for that in the real world. In Microsoft products, you can insert subscripts/superscripts a little more easily, but it’s still a fairly lengthy process involving menus and extra work. As a result, in practice, you almost always see this written as something like “R^2,” “R Squared,” or “R Sq.” Further, consider that R^2 is simple notation that everyone generally understands already, yet people still don’t spend the time to type it out the “right” way. If people can’t be bothered to express the superscript in R^2 the right way, why would they do it for your new notation that’s presumably (1) a lot more complex than R^2, and (2) a lot less commonly accepted than R^2?

[AndrewLouca]

Originally Posted by Lucy

And you're ignoring reinsurance.

I don't think I'm ignoring reinsurance. My goal with the first part of the book was to mathematically explain why insurance is necessary. So I try to see what it would take for a person, or group of people, to create their own plan from scratch. In the end, I list reasons why they can't (basically because it's a lot of work) and say this is where insurance comes in. I plan to include reinsurance, and other more traditional insurance concepts, in the next parts.

Originally Posted by Lucy

I think there's a great deal more research on risk pooling and diversification than you are aware of. That's not my area of expertise, and I can't suggest any particular text, but you might try poking around DARE.

I don't doubt for a second that there's more out there than I am aware of. Thanks for the suggestion

Originally Posted by Lucy

I looked at your text a bit, and was surprised at how foreign the words were to me. I've been a casualty actuary for decades, and you are using vocabulary I'm not familiar with. (To describe ideas that I am familiar with.) Is that on purpose?

Can I ask your opinion about the words that were foreign to you? Which ones in particular?

Originally Posted by Lucy

In general, I applaud your effort, although I'm dubious that anyone can coax the industry to uniform notation.

Thanks Yea, it might not be possible, but I'm having fun trying to make the notation. If that's all I get out of it the end, I guess I'll have to be happy with that

[AndrewLouca]

Originally Posted by nonactuarialactuary

Because they’re annoying to type with standard tools. Try typing R2 on Actuarial Outpost with the “2” properly formatted as a superscript. I don’t think you can do it unless you bring out the LaTeX formatting, and let’s be honest, nobody has time for that in the real world. In Microsoft products, you can insert subscripts/superscripts a little more easily, but it’s still a fairly lengthy process involving menus and extra work. As a result, in practice, you almost always see this written as something like “R^2,” “R Squared,” or “R Sq.” Further, consider that R^2 is simple notation that everyone generally understands already, yet people still don’t spend the time to type it out the “right” way. If people can’t be bothered to express the superscript in R^2 the right way, why would they do it for your new notation that’s presumably (1) a lot more complex than R^2, and (2) a lot less commonly accepted than R^2?

What do life actuaries do? They learn and are tested with a notation that uses superscripts and subscripts.

Eliminating the use of superscripts is too constricting for me. I don't think a good notation can be made without it. You're probably not going to like this, but I have plans for the subscript later on too.

[|B|rad]

Originally Posted by AndrewLouca

Can I ask why superscripts as identifiers should be illegal?

For me, superscripts are reserved for exponents only. Instinctively, L^G is L to the G power. Subscripts are the preferred place for identifiers.

I'm not the sort of person who reads a lot of actuarial papers, but the only place I can remember seeing a superscript ID is on the Siewart paper on XSLDFs, where he uses a superscript to identify the deductible.

[AndrewLouca]

Originally Posted by |B|rad

For me, superscripts are reserved for exponents only. Instinctively, L^G is L to the G power. Subscripts are the preferred place for identifiers.

I'm not the sort of person who reads a lot of actuarial papers, but the only place I can remember seeing a superscript ID is on the Siewart paper on XSLDFs, where he uses a superscript to identify the deductible.

Yea, I understand that concern and I was worried about it too.

There are two reasons I'm using the superscript as an identifier.

1. Variables should be read with context in mind. As far as I know, in actuarial science there is rarely the need to exponentiate random variables. So not using the superscript for some other piece of valuable information amounts to lost real estate.
2. I plan on using the subscript for a different identifier later. I could have put the G in the subscript now, but then I'd end up putting the other identifier in the superscript later and the same issue would arise.

[KS6392]

Originally Posted by AndrewLouca

In the context of the first part of the book, I define a set of policies to be "good" or "bad" based on the coefficient of variation of the total loss distribution specifically, if the coefficient of variation is less than 1, and the lower the better. The way I decide to use the coefficient of variation as a metric is gradually explained in chapters 1 through 4.

If I have two different groups, I say they are "better off" if the coefficient of variation of their combined loss distribution is less than the coefficient of variation of either of the separate group loss distributions. In the example I described above, when you add that single risk to the other 1,000, it's so different and causes the coefficient of variation to increase. For this case, the exact equation that describes this is as follows.

Let s and l represent the groups with the smaller and larger severities, respectively.
Let S(s) and S(l) represent their severities, so that S(s) < S(l)
Let N(s) and N(l) represent the number of risks having a small and large severity.

The two groups are "better off" combining into a single larger group if the following condition is satisfied

N(l)/N(s) > 1 - 2S(s)/S(l)

I just think there is so much nuance you're missing, I'll just leave it at that. I have less than 5 years experience as an actuary, so I would never claim to an expert. My opinion is that over-simplifying insurance problems can be useful as a teaching tool. But over-simplifying insurance problems to develop industry standards of notation and equations won't get you very far.

I do admire all the work you've done and think you have an honorable goal. Listening to the advice of others in this thread should be a good place to start for you, and I do recognize the courage it takes to put out something you've spent a lot of time on and take constructive criticism.