Spectrally negative Lévy processes with applications in risk theory

Optimal dividends in the dual model

“…The inversion of (9.5) withQ(ξ ) as in (9.10) does not appear to be easy. Yang and Zhang (2001) inverted the Laplace transform of the probability of ruin for the gamma process by using the first ten terms of the Maclaurin series of the logarithm in (9.10).…”

On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues

“…However, there exist various attempts in relaxing the usual assumptions. For example, the classical Poisson process used to model the number of claims has been replaced with other processes, see, e.g., [3,[5][6][7][8][9][10][11] etc. On the other hand, a dependency of the premium on the size of the surplus has been taken into account in [12].…”

On the expected discounted penalty function for a perturbed risk process driven by a subordinator

“…Hitting times, over-and under-shoots for Lévy processes have been extensively studied in an insurance context (or at least with insurance modeling in view). For example, the model in (1) is a subclass of the family of risk models discussed in Bertoin and Doney (1994), Yang and Zhang (2001), Morales and Schoutens (2003), Huzak et al (2004) and Doney and Kyprianou (2006). It is slightly more general than models discussed in and Morales (2004) since we are adding a Brownian motion to perturb the aggregate claim process.…”