General tax structures and the Levy insurance risk model

TL;DR

This paper extends the Levy insurance risk model by incorporating a more general tax structure, deriving key identities using excursion theory, and contributing to actuarial research on risk processes.

Contribution

It introduces a generalized tax structure in Levy risk models and derives fundamental identities using excursion theory, expanding the analytical tools available.

Findings

Derived two-sided exit problem identity

Calculated net present value of tax until ruin

Generalized Gerber-Shiu function

Abstract

In the spirit of previous of Albrecher, Hipp, Renaud and Zhou we consider a L\'evy insurance risk model with tax payments of a more general structure than in the aforementioned papers that was also considered in \cite{ABBR}. In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two sided exit problem, the net present value of tax paid until ruin as well as a generalized version of the Gerber-Shiu function. The method we appeal to differs from former works in that we appeal predominantly to excursion theory.