Assuming you've already stabilized the shot with the standard motion stabilization tracker in AE and now have a video track basically locked on the position of your main subject, you can create a null at your focus object and link the video track to it. Then use the null to gradually scale, move, rotate your footage to mimic the original motion in a more graceful, controlled manner, so that it still retains a bit of the natural motion, but stays relatively centered. If needed, there are a number of ways to fill in black edges created by rough stabilization. My favorite is precomping the stabilization and then using a plugin called Re:Fill by RevisionFX. It does a great job at filling in the holes in a similar way to how Photoshop's healing brush or content aware fill works. You could also try just duplicating the precomp and scaling it up just enough to fill the frame, then put a fast blur of about 5% and add some noise to it, and put it under you main comp. Then take an adjustment layer with a feathered vignette mask and apply the same fast blur and noise effects to blend the two comps together a bit. Plenty of other techniques exist for filling in edges, and for fast moving centrally focused footage, its pretty easy to get away with it.
The best technique depends entirely on the footage. Stabilize motion locks the tracked portion of the screen into position but this may result in an unnatural visual effect. Warp Stabilizer fixes rolling shutter problems and takes out camera shake. It the skier is fouling up the Warp Stabilizing you can delete the tracking points that are attached to the skier and you can also mess with the settings to improve the shot. My first inclination from the description would be to warp stabilize the shot and limit the scaling. Then I would probably render a DI (lossless 10 bit or better format digital intermediate) to do further processing on. Having the skier momentarily leave the frame is not necessarily a bad thing. If motion stabilizing and using a null to adjust position as the frame edges will help the shot then I would not use scale, but instead use Detail Preserving upscale to fix the edge problem. There are also some scripts available that will let you adjust the amount of stabilization you get with stabilize motion.
The other thing to consider, and probably the first thing that should be considered is how much of the shot do you need to tell your story effectively. Only you can answer that question. I tend to get really bored really quickly by long shots of someone just being chased by an action camera. Some of the things that are done may be truly amazing and best told in a single shot, but most of the time you'll get a better idea of what is going on by cutting the shot up.
If this single shot is extremely important you might want to look at this solution from my friend Mathias Muhl: Stabilize Motion Without the Need to Zoom