  We consider an insurance company modelling its surplus process by a Brownian
motion with drift. Our target is to maximise the expected exponential utility
of discounted dividend payments, given that the dividend rates are bounded by
some constant. The utility function destroys the linearity and the time
homogeneity of the considered problem. The value function depends not only on
the surplus, but also on time. Numerical considerations suggest that the
optimal strategy, if it exists, is of a barrier type with a non-linear barrier.
In the related article by granditz et al., it has been observed that standard
numerical methods break down in certain parameter cases and no close form
solution has been found.
  For these reasons, we offer a new method allowing to estimate the distance of
an arbitrary smooth enough function to the value function. Applying this
method, we investigate the goodness of the most obvious suboptimal strategies -
payout on the maximal rate, and constant barrier strategies - by measuring the
distance of its performance function to the value function.
