Snell envelope

The Snell envelope, used in and mathematical finance, is the smallest supermartingale dominating a . The Snell envelope is named after James Laurie Snell.

Given a filtered probability space ${\displaystyle (\Omega ,{\mathcal {F}},({\mathcal {F}}_{t})_{t\in [0,T]},\mathbb {P} )}$ and an absolutely continuous probability measure ${\displaystyle \mathbb {Q} \ll \mathbb {P} }$ then an adapted process ${\displaystyle U=(U_{t})_{t\in [0,T]}}$ is the Snell envelope with respect to ${\displaystyle \mathbb {Q} }$ of the process ${\displaystyle X=(X_{t})_{t\in [0,T]}}$ if

...
Wikipedia