The aim of this book is to summarize the obtained results of
investigation of the boundary problems tied with distributions of
boundary functionals for random processes and random walks with
independent increments considered in the fluctuation theory and to draw
attention to their connection with the risk theory. In the book special
attention is paid to Levy processes with hyperexponentially distributed
jumps. For them the unified prelimit and limit Pollaczeck-Khinchine
formulas are established. They are used in the investigation of
distributions of boundary functionals defining different characteristics
of the risk and queueing processes. This monograph will be useful to the
researchers working with probability theory and stochastic processes, in
particular for those who deal with boundary problems for Levy processes
and with their applications in risk theory, renewal theory, reliability
theory, queueing theory, financial and actuarial mathematics, and in
other applied areas. This book can be recommended to scientists,
engineers, students, and post-graduate students of economical and
mathematical specialities.