Snell envelope

The Snell envelope is a concept used primarily in the fields of stochastic control and optimal stopping theory. It provides a way to characterize the value of optimal stopping problems, particularly in scenarios where a decision-maker can stop a stochastic process at various times to maximize their expected payoff. Mathematically, the Snell envelope is defined as the least upper bound of the expected values of stopping times given a stochastic process. Formally, if \( X_t \) is a stochastic process (e.g.