On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier

The compound Poisson risk model with multiple thresholds

“…However, most papers in this area focus on a single threshold. See Albrecher et al (2005), Asmussen (2000, Chapter VII, Section 1), Bühlmann (1970), Gerber and Shiu (2006), Lin et al (2003), Lin and Pavlova (2006) and references therein. In this paper we discuss a general multi-threshold compound Poisson risk model.…”

The compound Poisson risk model with a threshold dividend strategy

“…Barrier strategies for the compound Poisson risk model have been studied in a number of papers and books, including Albrecher et al (2005), Albrecher and Kainhofer (2002), Bühlmann (1970, Section 6.4.9), Dickson and Waters (2004), Gerber (1972Gerber ( , 1973Gerber ( , 1979Gerber ( , 1981, Shiu (1998, 2005a), Højgaard (2002), Lin et al (2003), Paulsen and Gjessing (1997), and Segerdahl (1970).…”

On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times

“…A second important quantity in assessing the quality of a dividend barrier strategy is the distribution of the discounted sum of dividend payments until ruin. Traditionally, only the first moment of this distribution was considered, but for the classical risk model and constant barrier strategy Dickson and Waters (2004) recently studied arbitrary moments (an extension of this analysis to linear dividend barriers can be found in Albrecher et al (2005)). For a Brownian risk model, the distribution of dividend payments was investigated by Gerber and Shiu (2004a).…”