Univariate distributions: Introduction -- Counting distributions with recursion of order one -- Compound mixed Poisson distributions -- Infinite divisibility -- Counting distributions with recursion of higher order -- De Pril transforms of distributions in P10 -- Individual models -- Cumulative functions and tails -- Moments -- Approximations based on De Pril transforms -- Extension to functions in P1_ -- Allowing for negative severities -- Underflow and overflow -- Multivariate distributions: Introduction -- Multivariate compound distributions of Type 1 -- De Pril transforms -- Moments -- Approximations based on De Pril transforms -- Multivariate compound distributions of Type 2 -- Compound mixed multivariate Poisson distributions
Summary
Since 1980, methods for recursive evaluation of aggregate claims distributions have received extensive attention in the actuarial literature. This book gives a unified survey of the theory