Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Chapter TenDependence Concepts

10.1 Introduction to Concepts in Dependence for OpRisk and Insurance

This chapter is the first component of three chapters (Chapters 10–12) covering dependence modelling in OpRisk frameworks. These three chapters jointly cover a detailed account of the fundamental concepts that OpRisk practitioners should consider when developing dependence models for LDA OpRisk loss processes. In particular we first present an overview of dependence modelling approaches for LDA models which includes discussion on:

• Which components of the LDA model can dependence be added, such as between severities, between frequencies or between annual losses. This can be done explicitly via a parametric model such as a copula specification or via common shock frameworks, both of which are discussed in detail in the following chapters;
• A case study that provides an understanding of the basic impacts that dependence has in multiple risk LDA models. For instance, adding dependence between frequencies can induce dependence between annual losses etc. We provide some theoretical bounds on impacts of dependence for simple Poisson-LogNormal LDA models.

Having performed this case study, next we develop a mathematical description of the various notions of dependence that have been developed in the statistics literature, these include:

• Parametric model based Copula dependence;
• Multivariate Upper Negative (positive) Dependence, Lower Negative (positive) Dependence and Negative (positive) ...