You are given that the stochastic processes for two stocks, S$1,$ S$2$ are de$-$

scribed by:

dS$1($t$)$

S$1($t$)=$ $1$dt $+$ $1$dW $($t$)$

dS$2($t$)$

S$2($t$)=$ $2$dt $+$ $2$dW $($t$)$

with

$1=$ $2.$

Does the sum of the two stocks, S$1+$ S$2,$ follow a Geometric Brownian motion? Justify

your answer.

Exercise $4$ Assume a model for the stock price with the following dynamics

dS$($t$)=$ S$($t$)$dt $+$ dW $($t$).$

$1$