There was an excellent article on this in the Atlantic on the "Secret Fears of the Super Rich"[1]. The Atlantic article matches my (secondary) experience: while I am (emphatically!) not in this camp (I definitely need to work to pay my mortgage!), I have several close friends who are outrageously wealthy, and I have observed that their lives are not made less stressful by their wealth -- but the specifics change. For example, there is great anxiety about how to raise their kids, especially for those who were not themselves raised in wealth: they are torn between providing their kids those things that they did not themselves have while still having their kids seek those things that they themselves sought. This is much harder to square than it might sound, and I don't think that there's a pat answer -- though I would observe that the ones I know with the fewest problems are those that are the least ostentatious with their wealth.

None of this serves to answer the question of how they deal with it, but rather to confirm what we probably all know: while money makes certain things in life easier, it is not a cure for all ills.

[1] https://www.theatlantic.com/magazine/archive/2011/04/secret-...