Date: Friday 8th November 11-12:00 (Room ASHT-LR)
Abstract: Thiele's differential equation explains the change in prospective reserve in terms of premium income, benefit outgoings, mortality, and interest. It plays a fundamental role in safe-side calculations and other types of model comparisons. This no doubt helps explain why the generalization of Thiele's original result has been repeatedly the subject of scientific investigation. In this talk, I will report on recent developments with a focus on joint work with Marcus C. Christiansen from the University of Oldenburg. In particular, I will present a stochastic version of Thiele's equation with the novel feature that it supports any actuarial multi-state model. The corresponding comparison theorems offer a unifying and rigorous alternative to the actuarial folklore.