Mixed Poisson processes have until now been studied by scientists primarily interested in either insurance mathematics or joint processes. Often work in one area has been carried out without knowledge of the other. Mixed Poisson processes is the first book to be totally devoted to combining both these areas.
The first part of the book gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility and reliability properties; the second part of this is, to a greater extent, based on Lundberg's thesis.
Many newer results, such as characterizations in terms of thinning, random translations, Palm probabilities and symmetric distributions are given. Models for the risk fluctuations in an insurance company are considered in some detail.
Combining a rigorous mathematical approach with an informal discursive style, this book will be an invaluable source for probabilists, applied probabilists and actuaries, as well as graduate students and scientists in these areas.