Hi Everyone

I have some difficulties deriving the Stochastic Differential Equation for the following problem, any help or reference would be appreciated.

We are given a Brownian Motion $B_t$ and we note $M_t=\sup_{s\le t}B_s$. Moreover we have a smooth real valued function $F(t,x,y)$ (for example a $C^{1,2,1}$) over $\mathbb{R}^+\times \mathbb{R} \times \mathbb{R}^+$ and we are looking for the SDE followed by $F(t,M_t-B_t,M_t)$

I have a hard time trying to express $dF$.

Best regards