Snell envelope

The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process.

The Snell envelope is named after James Laurie Snell.

Given a filtered probability space

and an absolutely continuous probability measure

then an adapted process

is the Snell envelope with respect to

of the process

if Given a (discrete) filtered probability space

and an absolutely continuous probability measure

then the Snell envelope

is given by the recursive scheme where

is the join (in this case equal to the maximum of the two random variables).