Thanks! After drafting & reading S-1s for years, my superpower is skimming through quickly :)
On your first point, Lemonade's loss ratios are currently higher than industry average. This is likely tail weighted & driven by a few outlier claims, as their premiums underwritten are minuscule versus their large competitors. Lemonade has every incentive to continue pricing risk better, and ML is the perfect tool for this. Having spoken to CIOs (chief insurance officers) in the industry, the amount of data insurance companies generate is tremendous, and very quickly ML can spot correlations between price, claims payouts, frequency, etc. Harnessing the data as the largest insurcos are surprisingly manual & paper based, and asking the right questions to the machine is the hard part, but Lemonade has the advantage of being more nimble & not encumbered by the legacy tech stack.
Lemonade's original philosophy of taking a flat fee & donating the unpaid claims, was driven by disincentivzing fraud. They hired behavioral scientists, and this was big marketing push for their 1.0/1.5 platform. Insurance companies only have so many value levers to pull, and I think while not explicitly stated in the S-1, reading through publicly available posts & data show Lemonade is very much focused on pricing risk correctly and lower LR.
Regarding point 2, GAAP revenue (rarely use this term) is on the income statement throughout the S-1 (pg 18 is the first instance). Ceded premium to reinsurers is excluded from GAAP revenue (pg 103 has a table breakdown).
My thought is Lemonade is marketing GWP front and center on page 2, but shifting their biz to be heavily ceded to insurers, which lowers revenue. Yes, Lemonade is receiving a fee in exchange, and maybe lowering liabilities on their balance sheet. But, its not a great trade because 1) expensive CAC to cede it away, 2) they essentially become a broker, and brokers don't generate the multiples investors want, and 3) they don't take advantage of insurance float.