In mathematical finance, one often encounters parabolic PDEs typically through the Feynman-Kac representation theorem/formula. However, I'm curious are there interesting examples of Elliptic boundary value problems in mathematical finance?

I came across this post: https://quant.stackexchange.com/questions/60818/hyperbolic-and-elliptic-pdes-in-quant-finance?newreg=2a508218d11d4790aa2e565a596d8ff4

But I cannot find a clear mathematical formulation of a "perpetual exchange option" (whatever that is)...