  We disucss a statistical estimation problem of an optimal dividend barrier
when the surplus process follows a L\'{e}vy insurance risk process. The optimal
dividend barrier is defined as the level of the barrier that maximizes the
expectation of the present value of all dividend payments until ruin. In this
paper, an estimatior of the expected present value of all dividend payments is
defined based on ``quasi-process'' in which sample paths are generated by
shuffling increments of a sample path of the L\'{e}vy insurance risk process.
The consistency of the optimal dividend barrier estimator is shown. Moreover,
our approach is examined numerically in the case of the compound Poisson risk
model perturbed by diffusion.
