The tax identity in risk theory — a simple proof and an extension

By linking queueing concepts with risk theory, we give a simple and insightful proof of the tax identity in the Cramér–Lundberg model that was recently derived in Albrecher & Hipp [Albrecher, H., Hipp, C., 2007. Lundberg’s risk process with tax. Blätter der DGVFM 28 (1), 13–28], and extend the identity to arbitrary surplus-dependent tax rates.