Uncertainty and Probability Multiple Prior Martingale Theory

Optional Sampling Theorem

Theorem

Let(St) 0 ≤t≤Tbe a multiple prior supermartingale. Letσ≤τ≤T be

stopping times. Then

ess infP∈P EP[Sτ|Fσ]≤Sσ.

Remark

Not true without time consistency.