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 Q&A: "[Hyperbolic and Elliptic PDEs in Quant Finance](https://quant.stackexchange.com/q/60818/70758)" on the [Quantitative Finance StackExchange](https://quant.stackexchange.com), but I cannot find a clear mathematical formulation of a "perpetual exchange option" (whatever that is)...