Another thought:
Is there a way to have both an "insurance share" and an "investor share"?
Say 100 people want to buy 1 "investor share" each at $100 (using dollars because it's easier to visualize). You now added a $10,000 reserve to the insurance pot that also has all the monthly premiums. If total premium collected is $100,000, you now have $110,000 in the pool. If the claims for that month are $90,000 then $10000 is paid as a dividend back to the investors who now have a chance of earning money next month. Now if the next month you have the same $100,000 in premiums and $10,000 in investment reserves and the claims exceed $100k the investor gets no dividend. But if the following month $100k premium and $50k in claims, then $50k is split as a dividend to investors in the form of $5k each.
Of course these numbers could all be different and dividend payout could be a certain percentage of the unclaimed premiums, say 25%. That way it would add more to the following months reserve and so on....
You then could sell more shares each month that receive less dividend than the previous month so as to not dilute the original investors. Or only sell a limited number of shares per premium collected each month. And if premium drops, payouts will drop and investors could sell their share on a secondary market.
Is this possible?