A Lévy risk model with ratcheting and barrier dividend strategies

The expected present value of dividends is one the classical stability criteria in actuarial risk theory. In this paper, we consider two-layer $ (a, b) dividend strategy when process modeled by a spectrally negative Lévy process, such has an increasing rate surplus exceeds level a>0 $, and all excess over b>a as lump sum payments. Using fluctuation identities scale functions, obtain explicit formulas for net until ruin Laplace transform time to ruin. Finally, numerical illustrations are show impacts parameters on value.