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We consider an insurance company modelling its surplus process by a Brownianmotion with drift. Our target is to maximise the expected exponential utilityof discounted dividend payments, given that the dividend rates are bounded bysome constant. The utility function destroys the linearity and the timehomogeneity of the considered problem. The value function depends not only onthe surplus, but also on time. Numerical considerations suggest that theoptimal 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 standardnumerical methods break down in certain parameter cases and no close formsolution has been found.  For these reasons, we offer a new method allowing to estimate the distance ofan arbitrary smooth enough function to the value function. Applying thismethod, we investigate the goodness of the most obvious suboptimal strategies -payout on the maximal rate, and constant barrier strategies - by measuring thedistance of its performance function to the value function.

Suboptimal Control of Dividends under Exponential Utility