  In this paper we study the problem of stopping a Brownian bridge $X$ in order
to maximise the expected value of an exponential gain function. In particular,
we solve the stopping problem $$\sup_{0\le \tau\le
1}\mathsf{E}[\mathrm{e}^{X_\tau}]$$ which was posed by Ernst and Shepp in their
paper [Commun. Stoch. Anal., 9 (3), 2015, pp. 419--423] and was motivated by
bond selling with non-negative prices.
  Due to the non-linear structure of the exponential gain, we cannot rely on
methods used in the literature to find closed-form solutions to other problems
involving the Brownian bridge. Instead, we develop techniques that use pathwise
properties of the Brownian bridge and martingale methods of optimal stopping
theory in order to find the optimal stopping rule and to show regularity of the
value function.
