Let $W$ denote a Wiener process, $\displaystyle M_t = \max_{0 \le s \le t} W_s$ its running maximum. The martingale representation of $M$ is known explicitly:
$$M_T = \sqrt{\frac{2T} \pi} + \int_0^T 2\left(1 - \phi\left(\frac{M_t-W_t} {\sqrt{T-t}} \right)\right) \, \mathrm dW_t, $$
where $\phi$ denotes the pdf of a standard normal variable.
Question: do we have an explicit martingale representation for the running maximum of the Brownian bridge (conditioned to be zero at both ends of $[0,1]$)?