We revisit the optimal periodic dividend problem where dividend payments can only be made at the jump times of an independent Poisson process. Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level. In this paper, we show its optimality for a spectrally negative L\'evy model with a completely monotone L\'evy density. The optimal strategies and the value functions are concisely written in terms of the scale function . Numerical results are also given .
In this paper, we revisit the optimal periodic dividend problem , in which dividend payments can only be made at the jump times of an independent Poisson process. In the dual (spectrally positive L\'evy ) model, recent results have shown the optimality of a periodic barrier strategy , which pays dividends at Poissonian dividend-decision times , if and only if the surplus is above some level. In this paper, we show the optimality of this strategy for a spectrally negative L\'evy process whose dual has a completely monotone L\'evy density. The optimal strategies and value functions are concisely written in terms of the scale functions . Numerical results are also provided .
R
We
In this paper, we
R
where
, in which
R
Recent results have shown, in
In
A
L\'evy
A
recent results have shown
R
where dividends are paid at
, which pays dividends at Poissonian
A
,
R
its optimality
the optimality of this strategy
R
model with
process whose dual has
D
the
R
function
functions
R
given
provided