Question 3 Suppose that the risk-free rate follows the following stochastic process: drt = a(b - rt) dt + vg(t)dB. 1. Denote Rt = eatrt. Using Ito's lemma, find the expression for dRut. 2. Solve for Rt and rt. In your answer, Rt and rt should be written as a sum of a deterministic term and an Ito integral. 3. When t approaches infinity, what does Ert] approach to? Show your work. 4. Suppose that limt- e-2at fog(s)e2asds = 0. Show that Var[re] approach zero as t goes to infinity. 5. Show that limt- It = b in mean-square convergence