Unit-linked Insurance Policies in the Presence of Credit Risk

Abstract

In this thesis we derive a new version of Thiele's partial differential equation for computing the insurance reserves of unit-linked policies based on stochastic yields of bonds in a defaultable bond market. This is based on the Bielecki-Rutkowski credit model which can be considered as an extension of the Heat-Jarrow-Morton framework for modelling the term structure of interest rates. The equation is something that, to our knowledge, has not previously been presented in the existing literature.