A common way to hold a pen is with the thumb, index finger, and the last knuckle of the middle finger approximately the same distance from the tip, like this:

I find that this grip is not the most relaxed position. Allow me to elaborate.
After playing the piano for 30 minutes, I let my right hand hang at my side, using no energy. Here is my hand at its most relaxed state:



Notice that when I use no energy, the fingers are naturally curved, and the tip of the thumb is relatively far from the tip of the index finger.
If I put my right hand on a surface it falls into this shape:

If I put a pen in it, my right hand naturally holds the pen with this grip:

I feel that this grip puts the hand in a position closest to the most relaxed state. I can maintain this grip using no energy. The difference between this grip and the common grip is that in this grip, the thumb is placed farther away from the tip. Extending the thumb to where the common grip places it requires energy, and therefore does not yield the most relaxed grip.
Another thing one may try is simulating a longer nib by gripping higher with one's whole hand, like this:

This allows one to use less movement to write characters, and also lowers the writing angle.