The famous Snell envelope or something like it ! ! !

I was just reading about the famous Snell envelope in Financial mathematics. When I met this "Snelll" feature I was totally and completely confused weather I was reading mathematics, probability or something else.

Eventually it led me both to the lately used and announced as the important feature, the theory of martingales, and to the theory of operations research. Namely, I was reading about optimal stopping problems of stochastic processes and found some of the most interesting calculations and mixture of the twp fields.

It made me so curious that I ended up reading some new paper about not one, but multiple optimal stopping times problem in the American option trading system. The idea is to find the supremum of both conditional and unconditional mathematical expectation of the reward function at some random time. Utterly very very interesting theory...... think about it