Stochastic Processes and
Advanced Mathematical Finance
Homework 9

Steve Dunbar

Due Mon, November 22, 2010
  1. Let W1(t) be a Brownian motion and W2(t) be another independent Brownian motion, and ρ is a constant between 1 and 1. Then consider the process X(t) = ρW1(t) + 1 ρ2W2(t). Is this X(t) a Brownian motion?
    1. Differentiate the c.d.f. of Ta to obtain the expression for the p.d.f of Ta.
    2. Show that E Ta = for a > 0. (Hint: use the Integral Comparison Test, see any calculus book in the section on Improper Integrals.)