Welcome to Switzerland. Just about everything is subject to the non-competitive economy here, petrol and bottled water excepted.

I have had life insurance with Norwich Union (now Aviva) in the UK since the late 90s, which has continued to cover me wherever I've lived in the world (three countries since then). As a bit of a bonus (from my perspective), the premiums are fixed (but of course so is the insured amount).

I'd imagine that quite a few insurers would offer global insurance.

Good luck with the insurance, and with buying things here in general!