I went through the notes from my adviser today. Most were straightforward corrections or clarifications. A few require some more thought. One, in particular, cuts directly to our version of "truth" when issuing a query.
Are we viewing the query sum as a true value or the realization of a random variable? Stated another way, is this truly a finite population with a fixed query sum, or is it just a really large sample from a larger population. I have been treating it as a finite population, but I can see instances where the other treatment makes at least as much sense.
For the purposes of projecting the capital needs of the company, it is definitely a finite population. Our portfolio of policies is known and finite. Sure, we may get more, but the question at hand is how to cover our current inventory.
When we look to experience studies, however, that stance becomes harder to defend. Experience studies look at actual cash flows to see how well they match the projections. If the two are diverging, it may indicate a problem with our models and we would want to update pricing of new business to reflect that. In this case, we are using our own inventory simply because that's the best data we have. If we had cash flows from a competitor, we'd happily look at that as well. In that framing, our own data set is really a sample of all the possible policies in the world.
I'd rather stick with the finite model, simply because I think it's been less explored so our method has more novelty. In particular, while it's hardly a profound result, I like my formula for the distribution of our statistic relative to the true sum. It converges to the distribution suggested by the Central Limit Theorem as the number of observations gets very large, but it is distinct in interesting ways. However, if we really run into something intractable, we could switch and still have something useful.
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