A financial math problem concerning brownian motion modeling.

Consider the following market model for three assets: ds; = Sordt, dS7 = S; (pldt +0dB/), ds} = $} (undt + 02 (pdB; + V1 p?dB})), where r, M1, M2,01,02 > 0, and pe (-1,1) are constants and Bl and B2 are two independent Brownian motions. (i) Construct an EMM Q for this market model. Is it unique? (ii) Derive the PDE for the pricing function F(t, 81, 82) for the option G max{aS1,6S{}, where a, b> 0 (thus, up to the scaling factors a and b, we obtain the maximum of the two stock prices at time T). (iii) Use the reduction of the state space technique (see Section 13.4 in Bjrk) and the Black-Scholes formula to find a solution F(t, 81, 82) of the PDE derived in (ii). Consider the following market model for three assets: ds; = Sordt, dS7 = S; (pldt +0dB/), ds} = $} (undt + 02 (pdB; + V1 p?dB})), where r, M1, M2,01,02 > 0, and pe (-1,1) are constants and Bl and B2 are two independent Brownian motions. (i) Construct an EMM Q for this market model. Is it unique? (ii) Derive the PDE for the pricing function F(t, 81, 82) for the option G max{aS1,6S{}, where a, b> 0 (thus, up to the scaling factors a and b, we obtain the maximum of the two stock prices at time T). (iii) Use the reduction of the state space technique (see Section 13.4 in Bjrk) and the Black-Scholes formula to find a solution F(t, 81, 82) of the PDE derived in (ii)