There have already been some notable successes; in 2017, Lemonade used a chatbot to settle a claim in three seconds – a thousand times faster than its quickest claims adjuster.
In the longer term, the sky's the limit. Imagine a future in which you have a car accident and the car reports the claim for you. The sensors in your car will tell your insurer the nature of the damage and even how much the repairs will cost. Your insurer can then arrange a mechanic to start the repairs straightaway.
Similarly, if something goes wrong at home, such as a water leak, sensors connected to the internet can switch the water off remotely, minimizing damage and reducing the cost of a claim.