Processes with independent increments in risk theory (Q2880788)

This book is a revised and extended version of the author's book [Boundary value problems for processes with independent increments in risk theory. Kyïv: Instytut Matematyky NAN Ukraïny (2007; Zbl 1199.60001)]. Updated results on investigations of distributions of boundary functionals for processes with stationary independent increments and theirs application in risk theory and in financial mathematics are included in this book. Recent results (obtained by author during the last 3 years) amplify Chapters 3, 4, 6, 7 of the mentioned monograph, and they are included in n. 3.5-3.6, n. 4.4, and nn. 6.4-6.5, n. 7.4 of the new extended version. Their complements are concerning mainly some functionals for queuing processes and integer-valued Poisson processes. Some of complements are connected with generalizations of the Pollachek-Khinchine formula, cumulant representation of roots of the Lundberg equation and with the simplifications of Spitzer's formula for semi-continuous (almost semi-continuous) processes. Risk processes are described by compound Poisson processes (with diffusion or without it), by binomial processes (which are reduced to random walks), sometimes by Poisson processes with a reflection. The main characteristics investigated in risk theory are connected with distributions of different boundary functionals of processes with independent increments (extrema on finite intervals, absolute extrema, overjump functionals, sojourn times and others).NEWLINENEWLINE Sometimes in papers and monographs on risk theory a lot of probabilistic problems are studied without mentioning the connections with the corresponding results for boundary problems of processes with stationary and independent increments. The aim of the book is to summarize the results on investigations of distributions of all boundary functionals for processes with independent increments and to attract attention on the connection between problems in risk theory and boundary problems for the corresponding processes and random walks.NEWLINENEWLINE The monograph will be useful for researchers in probability theory and in the theory of stochastic processes who deal with boundary problems for random processes (especially for processes with stationary independent increments) and with their applications in risk theory, in renewal and reliability theory, in actuarial mathematics, in queuing theory and in other applied areas.NEWLINENEWLINEThis book can be recommended to scientists, engineers, students and post-graduate students of economics and mathematical disciplines, who are interested in applications of probabilistic methods in insurance, in storage and reliability models and in different fields of economics.