Suppose you construct a portfolio of two stocks, whose values $A$ and $B$ are modelled as a Bachelier process: $$dA = \sigma_A dW_A(t) \text{ and } dB = \sigma_B d W_B(t).$$ Each of the stock prices is driven by a different Brownian motion with correlation $\rho$. The value of the portfolio is $P = A + B$. I want to model this portfolio; so I started like this: $$dP =dA + dB = \sigma_A dW_A(t) + \sigma_B d W_B(t),$$ however, I feel like you can include the correlation somehow, but I don't know how. Any ideas?
Thanks in advance.