Uncertainty and Probability American Straddle

American Straddle in the Bachelier Model for Drift

Ambiguity

g–HJB equation: in the continuation set

vt+^12 vxx−κ|vx|= 0

Verification: solve the standard optimal stopping problem underP∗.

There, the HJB equation reads

vt+^1

2

vxx−κsgn(x)vx= 0

Show sgn(vx) = sgn(x), then this equation becomes theg–HJB equation

and we are done.