Ruin Problems and Tail Asymptotics
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived. An important part of this work is the construction of partial eigenfunctions for the infinitesimal generator of the process. Furthermore asymptotic results for the ruin probability are found. In a different setup concerning a model like the classical Cramér-Lundberg model but with parameters governed by an underlying Harris recurrent Markov process some asymptotic results for the ruin probability are derived. Finally, a paper, which is separate in content from the rest of the thesis, treats a RESTART problem in the situation, where failures occur with decreasing intensity.
Thesis advisor: Søren Asmussen