On Matrix-analytic Methods and on Collective Risk in Life Insurance
Jakob Riishede Möller
Centre for Mathematical Sciences
Two of the classical topics in applied probability, queues and insurance
models, are investigated. The queueing models considered are matrix-analytic
models and the problem we consider in insurance mathematics is the tail behavior
of the ruin probability in life insurance models.
Typical models and key results of matrix-analytic methods are presented.
Some of these models describe arrival processes and service time distributions,
respectively, and some models are generalizations of queue length
processes/waiting time processes.
One of the results of the thesis deals with an integral equation for the
waiting time distribution in many-server queues. A complete solution and
numerical examples are given.
Some results describe tail asymptotics for distributions of the queue length
in some matrix-analytic models. Models where the increments of the queue
length have subexponential tails and light tails, respectively, are described.
Finally, the ruin probability in some life insurance models is characterized
by means of the adjustment coefficient, that is, the tail behavior of the
ruin probability is investigated. In particular, the effect of the premium
principle used is investigated. Numerical examples are given.
queues, insurance mathematics, matrix-analytic methods, subexponential
distribution, exponential change of measure, many server queues, life insurance,
adjustment coefficient, premium principle.