  The optimization criterion for dividends from a risky business is most often
formalized in terms of the expected present value of future dividends. That
criterion disregards a potential, explicit demand for stability of dividends.
In particular, within actuarial risk theory, maximization of future dividends
have been intensively studied as the so-called de Finetti problem. However,
there the optimal strategies typically become so-called barrier strategies.
These are far from stable and suboptimal affine dividend strategies have
therefore received attention recently. In contrast, in the class of
linear-quadratic problems a demand for stability if explicitly stressed. These
have most often been studied in diffusion models different from the actuarial
risk models. We bridge the gap between these patterns of thinking by deriving
optimal affine dividend strategies under a linear-quadratic criterion for a
general L\'evy process. We characterize the value function by the
Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the
optimal controls to the classical objective of maximizing expected present
value of future dividends. Thereby we provide a framework within which
stability of dividends from a risky business, as e.g. in classical risk theory,
is explicitly demanded and explicitly obtained.
