Dividend Payments in a Risk Model Perturbed by Diffusion with Multiple Thresholds

Abstract

We consider a perturbed renewal risk model where the interclaim times are phase-type distributed and the dividend payment is a step function depending on the current surplus level. We obtain the integro-differential equations with boundary conditions for the moment-generating functions and the moments of arbitrary order of the present value of all dividend payments until ruin. Explicit expressions for the expected discounted dividend payments are derived if the claim amount distribution belongs to the rational family. Last, we present an example to show how the results are applied.

Dividend optimization for jump–diffusion model with solvency constraints

“…Under the assumption that the surplus of an insurance company is described by a Brownian motion with drift, Asmussen and Taksar (1997) study an optimal dividend problem for an insurance company by applying the singular stochastic control theory. For other related works we refer to Asmussen et al (2000), Taksar (2000), Paulsen (2007Paulsen ( , 2008, Schmidli (2008), Wei et al (2010), Bai et al (2012), Zhang (2012), Jiang and Yang (2013), and references therein. For the case of surplus process being spectrally negative Lévy process and the case of involving transaction costs, we refer to Loeffen (2008Loeffen ( , 2009 and Hunting and Paulsen (2013) and references therein.…”

The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence

“…[8] considered a perturbed MAP risk model with dividend barrier strategies. [15] investigated dividend payments in a perturbed renewal risk model with multiple thresholds where the inter-claim times are phase-type distributed. The above-mentioned literatures assumed that claim amounts are independent of inter-claim times.…”