In an universe we have two assets and a predictor: $\frac {dS_{1,t}}{S_{1,t}}=(\mu_{1,1}+\mu_{1,2}X_t)dt+\sigma_{1,1}dB_{1,t}+\sigma_{1,2}dB_{2,t} $ $\frac {dS_{2,t}}{S_{2,t}}=(\mu_{2,1}+\mu_{2,2}X_t)dt+\sigma_{2,1}dB_{1,t}+\sigma_{2,2}dB_{2,t} $
$dX_t=\theta(\bar X-X_t)dt+\sigma_X dB_{1,t}$
Find the price of european put at T on assets $S_1$ in a complete and no arbitrage market with riskfree rate r.
I know the how to solve the problem without the mean-reverting process--just use the $S_2$ to hedge away the brownian motion. However, the Ornstein-Uhlenbeck doesn't have close-form solution, which stopped me in the half way. How should I do with this problem?