Loss Data Analysis

1Introduction

In this short chapter we shall do two things. First, we briefly describe the generic problem that eventually leads to the same typical numerical Laplace inversion problem, and second, we give a summary of the contents of this book.

1.1The basic loss aggregation problem

Consider the following compound random variable:

$S={\displaystyle \sum _{n=1}^N{X}_n},\left(1.1\right)$

in which N is an integer valued random variable and the X n are supposed to be positive random variables, independent identically distributed and independent of N, all of which are defined on a common probability space (Ω, ℱ, P). The product space structure from the underlying probability space comes to mind as the obvious choice. That is, we may consider Ω = ℕ × [0, ...