Recursions for Compound Distributions

A Method for Evaluating Compound Distributions without Recursions

Measure Concentration for Compound Poisson Distributions

Abstract: We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal polynomial decay. Sim...

Panjer recursion versus FFT for compound distributions

Numerical evaluation of compound distributions is an important task in insurance mathematics and quantitative risk management (QRM). In practice, both recursive methods as well as transform based techniques are widely used. We give a survey of these tools, point out the respective merits and provide some numerical examples.

Recursions for the Individual Model

Recently, Waldmann considered an algorithm to compute the aggregate claims distribution in the individual life model which is an efficient reformulation of the original exact algorithm of De Pril. In this paper we will show that in practice the approximations as proposed by De Pril are still more efficient than the exact algorithm of Waldmann both in terms of the number of computations required...

Recursions for statistical multiple alignment.

Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne-Kishino-Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignment at nodes in a tree. Depending on whether the complete realization of this Markov chain is decomp...