Question 4: On continuous-time [25 marks] Please answer the following questions, justifying your answers: a. Suppose 11, is a Brownian motion. Is the stochastic process l’,=2+t+en•
a martingale?
b. The risk-free interest rate r, in the Vasicek model follows the Ornstein-Uhlenbeck process. It is known that r, can be expressed as a stochastic integral
= 0.03 + (r0 — 0.03) Caw + 0.002(c°81.1 (“MIL
where It is a Brownian motion. Find the distribution of r. as of time