  We consider the dividend maximization problem including a ruin penalty in a
diffusion environment. The additional penalty term is motivated by a constraint
on dividend strategies. Intentionally, we use different discount rates for the
dividends and the penalty, which causes time-inconsistency. This allows to
study different types of constraints. For the diffusion approximation of the
classical surplus process we derive an explicit equilibrium dividend strategy
and the associated value function. Inspired by duality arguments, we can
identify a particular equilibrium strategy such that for a given initial
surplus the imposed constraint is fulfilled. Furthermore, we illustrate our
findings with a numerical example.
