How are automated cars a threat to car insurance?
Here's how I assume it would work. For an insurance company to be profitable, premium payments need to be larger than claims payouts.
If we assume self-driving cars will be a lot safer, then claims payouts will drop significantly. If we assume insurance companies compete with each other, then that opens up their margins and eventually that will contract again as they all lower premiums to compete.
The end result is a smaller total amount of cash flowing through those businesses. The whole industry will contract because there's just less need for it to exist. You can think of insurance companies like a farm that harvests risk. With less risky automobiles, there's simply less crop for them to reap.
http://fortune.com/2015/10/07/volvo-liability-self-driving-c...
What driver exactly am I insuring?
The same reason property owners in general by liability insurance for liabilities that may occur to do property they own.
> What driver exactly am I insuring?
Most likely, you're insuring against liability resulting from your obligation as the owner (or leaseholder-in-possession, in the case of a lease) of the autonomous vehicle to maintain the vehicle in condition for safe operation and to remove it from operation if that is not possible.
The risk you're insuring is negligent or wilful bad driving, and risks inherent in the technology.
All of the above is true for self-driving cars, only with much-reduced negligent risk. The premiums will go down significantly, but the consumer motivation and the public policy interest to have insurance will remain. It may be assumed by the manufacturers for 100% self-driven cars, but insurance of outsized payouts is not something unique to the current iteration of the car industry.