The value of a share at time t is Where x 0 > 0 and {D(t), t ≥ 0} is a Brownian motion with positive drift parameter μ and variance parameter σ 2 . At time point t = 0 a speculator acquires an...

The value of a share at time t is

Where x₀
> 0 and {D(t), t ≥ 0} is a Brownian motion with positive drift parameter μ and variance parameter σ². At time point t = 0 a speculator acquires an American call option on this share with finite expiry date . Assume that

(1) Why does the assumption make sense?

(2) When should the speculator exercise to make maximal mean undiscounted profit?