Thanks for your question! It is expected that some insurance companies may initially decline to insure fully automated or driverless vehicles, based on the perceived risk to insure them and the lack of data to prove their safety. Further on in the future, though, driverless cars may eventually be considered a safety feature like seat belts or airbags. This is interesting speculation, and it will certainly evolve as more data becomes available so that insurance companies can properly rate the level of risk associated with driverless vehicles.
For some more information about driverless cars, check out this article: All About Self-Driving Cars.
