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

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