  In this paper, we model the cash surplus (or equity) of a risky business with
a Brownian motion. Owners can take cash out of the surplus in the form of
"dividends", subject to transaction costs. However, if the surplus hits 0 then
ruin occurs and the business cannot operate any more.
  We consider two types of dividend distributions: (i) periodic, regular ones
(that is, dividends can be paid only at countable many points in time,
according to a specific arrival process); and (ii) extraordinary dividend
payments that can be made immediately at any time (that is, the dividend
decision time space is continuous and matches that of the surplus process).
Both types of dividends attract proportional transaction costs, and
extraordinary distributions also attracts fixed transaction costs, a realistic
feature. A dividend strategy that involves both types of distributions
(periodic and extraordinary) is qualified as "hybrid".
  We determine which strategies (either periodic, immediate, or hybrid) are
optimal, that is, we show which are the strategies that maximise the expected
present value of dividends paid until ruin, net of transaction costs.
Sometimes, a liquidation strategy (which pays out all monies and stops the
process) is optimal. Which strategy is optimal depends on the profitability of
the business, and the level of (proportional and fixed) transaction costs.
Results are illustrated.
