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

For spectrally negative Lévy risk processes we consider a generalized version of the De Finetti's optimal dividend problem with fjxed transactioncosts, where the ruin time is replaced by a general drawdown time in theframework. We identify a condition under which a band{type impulse dividendstrategy is optimal among all admissible impulse strategies. As a consequence,we are able to extend the previous results on ruin time based impulse dividendoptimization problem to those on drawdown time based impulse dividend optimizationproblems. A new type of drawdown function is proposed at end, andvarious numerical examples are presented to illustrate the existence of thoseoptimal impulse dividend strategies under different assumptions.