GE is in real trouble to fund pension obligations after prioritizing stock performance first (and using cash for buybacks instead of the pension). Tens of thousands of GE workers could join millions from other companies and potentially lose their pension if GE can't find the money to fund it properly. Their shortfall is 30%.
The Chevron shortfall appears to be 25% (someone can correct this). The bigger risk for Chevron is that we are directly in the sights of a couple of the most disruptive technologies out there - electric cars and solar power coupled with battery advances. Chevron could conceivably disappear within ten years, a la Kodak, driven out of business by the digital revolution.
Keep this in mind when choosing an annuity. You can't change your mind later.