Question:
Let $(\Omega,\mathcal F,\mathbb P)$ be a probability space.
Let $Y_t=(Y_1(t),Y_2(t))$ be the solution to the SDE:
$dY_1=\beta_1dt+dB1+2dB2+3dB3$
$dY_2=\beta_2dt+dB1+2dB2+2dB3$
Where $\beta_{1,2}$ are bounded , $B1,B2,B3$ Brownian motions.
Prove that there are infinitely many equivalent martingale measures adapted to the filtration.
My Idea:
I want to use Radon Nikodym to establish the existence of measure change $Z=dQ/dP$
Then to use Girsanov's theorem to show that this could be done so Q is an equivalent martingale measure.
Then I want to apply this to the fact that the system have infinitely many solutions
My questions:
a. Is this method correct?
b. Is the system of 2 equations with 5 variables and so has infinitely many solutions?
c.Or maybe it is the lack of boundary condition the gives the system infinitely many solutions?