Consider the SDE where W is a one-dimensional Brownian motion and a and σ are constants. By applying It o’s formula to the process show that the unique solution to this SDE is given by Assuming a...

Consider the SDE

where W is a one-dimensional Brownian motion and a and σ are constants. By applying It o’s formula to the process

show that the unique solution to this SDE is given by

Assuming

a constant, specify the distribution of X_t.

Black–Scholes economy

Consider the Black–Scholes economy as defined in for the finite time interval

the price process

satisfies