This exercise deals with obtaining martingales. Suppose Xt is a geometric process with drift μ and diffusion parameter σ.
(a) When would the e-rt Xt be a martingale? That is, when would the following equality hold.
(b) More precisely, remember from the previous derivation that
Or, again,
Which selection of μ would make e-rt Xt a martingale? Would
μ = r
work?
(c) How about
μ = r + σ2?
(d) now try:
μ = r - ½ σ2.
Note that each one of these selections defines a different distribution for the e-rtXt
