It's probably fair to say that insurance has been slightly slow to the Fintech/blockchain party, compared to its banking peers. However, the FT reported yesterday that blockchain is being used in a live product.
A company called Blem worked with Z/Yen (a blockchain consultancy) to develop technology that will permanently record details of claims, so that insurers and reinsurers can accurately divide the costs between them. In particular, the timestamping aspect is seen as critical as it provides certainty to the reinsurer that information existed at a certain point in time and has not changed.
I'd not really thought about this potential use of Blockchain, so I'm excited to see what else is out there. The FT suggests that blockchain could be used in fraud prevention and commercial insurance policies (to record details of transactions that take place).