This paper considers the optimal dividend payment problem inpiecewise-deterministic compound Poisson risk models. The objective is tomaximize the expected discounted dividend payout up to the time of ruin. Weprovide a comparative study in this general framework of both restricted andunrestricted payment schemes, which were only previously treated separately incertain special cases of risk models in the literature. In the case ofrestricted payment scheme, the value function is shown to be a classicalsolution of the corresponding HJB equation, which in turn leads to an optimalrestricted payment policy known as the threshold strategy. In the case ofunrestricted payment scheme, by solving the associated integro-differentialquasi-variational inequality, we obtain the value function as well as anoptimal unrestricted dividend payment scheme known as the barrier strategy.When claim sizes are exponentially distributed, we provide easily verifiableconditions under which the threshold and barrier strategies are optimalrestricted and unrestricted dividend payment policies, respectively. The mainresults are illustrated with several examples, including a new exampleconcerning regressive growth rates.
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