Stress
You'll be dealing with customers who feel like the claims adjustment process isn't moving fast enough, or that they aren't getting paid enough for their claim, and so they'll take their wrath and frustration out on you. You'll be working for a corporate entity that would prefer not to have to pay out on any claims at all, thank you very much.
You'll work long hours. You may have to travel and be away from home for weeks or months at a time, if the disaster you're working is particularly nasty. You'll get up close and personal with heartbreak and despair.
So, yes, this job can be stressful.