Exercise . Consider the two general stochastic processes x = (xt) and x = (xt) defined by the dynamics dxt = t dt + t

Exercise . Consider the two general stochastic processes x = (xt) and x =

(xt) defined by the dynamics dxt = μt dt + σt dzt, dxt = μt dt + ρtσt dzt +

.

 − ρ

t σt dzt,

where z and z are independent one-dimensional standard Brownian motions.
Interpretμit, σit, and ρt. Define the processes y = (yt) andw = (wt) by yt = xtxt and wt = xt/xt. What are the dynamics of y and w? Concretize your answer for the special case where x and x are geometric Brownian motions with constant correlation, that is μit = μixit, σit = σixit, and ρt = ρ with μi, σi, and ρ being constants.