Two examples that come to mind: Facebook developing their "check in as safe" feature for disasters, and Uber adding one-sided surge pricing so that they can respond to post-disaster demand without raising prices. Uber's move was mostly about fixing a prior oversight, but Facebook's has provided some fairly novel benefit. Basic mobile internet is both more widely available and more disaster-proof than other communications, so it's a welcome improvement on "people flood the phone system trying to call loved ones".
That said, the biggest opportunities here seem to be in disaster-awareness from developers of existing software. IBM's pitch of "come create novel software for disaster response" looks rather less convincing.
I think autonomous systems and AI can greatly reduce the cost of disaster recovery. Search and rescue using drones for example, the NASA Autonomy Incubator was working on a system like that with MIT while I was there [1].