Uncertainty and Probability Optimal Stopping Rules

Minimax Theorem

Question: what is the relation between the Snell envelopesUPfor fixed

P∈Pand the multiple prior Snell envelopeU?

Theorem

U= ess inf

P∈P

UP.

Corollary

Under our assumptions, there exists a measure P∗∈Psuch that

U=UP∗.The optimal stopping rule corresponds to the optimal stopping

rule under P∗.