Exercise 13.6 For a standard Brownian motion {z(t)} and any IR, let Prove that {V

Exercise 13.6 For a standard Brownian motion {z(t)} and any β ∈ IR, let

Prove that {V (t)} is a martingale with respect to the Brownian filtration.
Also, let {N(t)} be a Poisson process with intensity λ > 0. Show that the following are martingales with respect to {FN t }, where FN t = σ(N(s), s ≤ t).

Transcribed Image Text:

= V(t) exp z(t) - exp{8=(0)2+} t 0.