Uncertainty and Probability American Straddle

American Straddle in the Bachelier Model for Drift

Ambiguity

Suppose we want to stopXt=Wtunderκ–ambiguity for an interest rate

r>0, i.e.

maxτ E(|Xτ|e−rτ).

Claim: under the worst–case measureP∗, the processXhas dynamics

dXt=−sgn(Xt)dt+dWt∗

for theP∗–Brownian motionW∗.