Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk

CHAPTERNINE

Recursions for Distributions of LDA Models

This chapter develops and presents a range of recursive numerical and statistical evaluation procedures for assessing the properties and providing alternative statistical estimators for the quantities of interest proposed in previous chapters relating to tail functionals of compound processes. The primary interest will be on the estimation of the tail of the compound process and assessment of the asymptotic approximations developed previously. The basic sections proposed in this chapter will consider recursions that fit into one of the following four categories:

1. Recursions for discretized severity n-fold convolutions;
2. Recursions for continuous severity n-fold convolutions;
3. Recursions for discretized severity compound process LDA models; and
4. Recursions for continuous severity compound process LDA models.

9.1 Introduction

The applications of the recursions considered in this chapter, will be in analysis of the results presented in previous chapters regarding closed-form approximations for the tail of a compound process and the resulting risk measure approximations, which are now studied from a statistical perspective. The reason for this is that although these results are important closed-form solutions, in practice, the implementation of these results can be difficult and challenging. The challenges can arise from a number of areas, either because the models considered do not adequately satisfy all the assumptions utilized ...