Consider the stochastic process Xt, given by Xt= e^(Wt), where Wt is a Brownian motion.

Problem 3. Feynman-Kac application We consider the stochastic process (XJQD given by X; = cw where (M) is a Brownian motion. Part A. (a) Determine the stochastic differential equation satised by the process (Xt). (b) We want to determine g[t,Xt) = E [X] Use Feynman-Kan formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in 9:. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution