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In this paper, we consider the mixed ratcheting-periodic dividend strategiesfor spectrally negative L\'{e}vy risk model, in which dividend payments canboth be made continuously without falling and discretely at the jump times ofan independent Poisson process. The expected net present value(NPV) ofdividends paid up to ruin and the Laplace transform of the ruin time areobtained by using L\'{e}vy fluctuation theory. All the results are expressed interms of scale functions. Finally, numerical results for Brownian motion withdrift are given.

Spectrally negative L\'{e}vy risk model under mixed ratcheting-periodic dividend strategies