GENERAL DRAWDOWN BASED DIVIDEND CONTROL WITH FIXED TRANSACTION COSTS FOR SPECTRALLY NEGATIVE LEVY RISK PROCESSES

For spectrally negative Levy risk processes we consider a generalized version of the De Finetti's optimal dividend problem with fixed transaction costs, where the ruin time is replaced by a general drawdown time in the framework. We identify a condition under which a band-type impulse dividend strategy is optimal among all admissible impulse strategies. As a consequence, we are able to extend the previous results on ruin time based impulse dividend optimization problem to those on drawdown time based impulse dividend optimization problems. A new type of drawdown function is proposed at end, and various numerical examples are presented to illustrate the existence of those optimal impulse dividend strategies under different assumptions.