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Let $dX_t=u(t,w)dt+dB_t$, where $dB_t$ is a Brownian Motion, $u$ is bounded and measurable with respect to the filtration $F_t$ and $u$ be an ito process on $(\Omega, \{\mathcal{F}\},\mathcal{P})$. Find a martingale $M_t$ s.t. $M_0=1$ and $Y_t=X_tM_t$ is an $\mathcal{F}_t$-martingale.

It is easily derived that $X_t=X_0+\int^t_0 u(s,w)ds+B_t$.

  • 2
    Could you also define $w$ ?2011-11-14
  • 2
    Try Girsanov theorem2011-11-14
  • 0
    $u(t,w)$ is some ito process and w is just some parameter2011-11-14
  • 0
    I don't think $M_t=1$ will work, since $X_t$ is not a martingale2011-11-14

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