Let me try to address this one (sorry this will be lengthy):
Example 1: Health insurance:
Imagine that you convert the hospitals onto a blockchain in which you store all of the patients data, I.e. you have an undisputable history of when the patients received treatment, what kind of illness was diagnosed, who diagnosed, who signed off on treatment, what treatment was given, why, how and when. Obviously this would be in a permission based blockchain to ensure confidentiality and privacy of patient data as well as safeguard patient / doctor confidentiality and there would be smart contracts in place to regulate who can gain access to what information, and under which permissions access would be granted or denied.
This could serve as a blockchain that can be shared across hospitals, across borders and across language barriers so that if the patient is in a different country / hospital they would have the possibility to look at the patient’s history, understand his allergies, ongoing medication, etc. etc.
How would this benefit insurance companies? They could equally get access to this blockchain (with limitations obviously) and decide on the correct insurance plan and insurance premium for this patient. Have a pre-existing condition? No problem it is there, in the blockchain, so the insurance company knows this and can tailor your health insurance accordingly.
People with no pre-existing conditions would benefit from lower premiums as a result while those with pre-existing conditions could still be fully insured as there is proof of clear treatment, follow up and resolution, all in that single blockchain. Those cheating the system by lying to their insurance company would lose out to a degree (I know we all do it) but the potential benefits of such a blockchain outway the disadvantages, provided you create the right, secure, safe and confidential environment through various smart contracts.
You could agree on statutes of limitations for pre-existing conditions and yes, insurance companies could easily reduce a vast amount of paperwork at the same time by adding billing and settlement through the same blockchain. This would resolve massive amounts of treatment settlement disputes, reduce vast amount of time and money spend on credit and collection for both parties (hospitals only receive a fraction of what they’re actually due from insurance companies).
You could add in pre-approval for services and treatment, etc.
Additionally they can get rid of a lot of current paperwork around applications, etc.
There’s even more benefits for the hospital to this but that’s outside the realm of the question.
Example 2: Car insurance
Imagine that your driving behaviour is recorded on a blockchain, I.e. each time you get a ticket or accident, it is recorded. Each time you change cars it is recorded, how often you service the vehicle, etc.
Similar to the hospital, the insurance company could create a completely customised and personalised car insurance for you, catering to your needs and financial means; as they would have clear visibility on the risk factors of insuring you.
In many countries now, people below a certain age, get slapped with a high premium, simply because their age groups are reckless drivers. A blockchain could help those prove their good (or bad) driving behaviour to the insurance company and get adjusted premiums as a result; which in turn could be loaded into the blockchain for future use.
So yep, I can see a vast amount of benefits for this for insurance companies and a wide range of other industries.