Motivation for Heavy-Tailed Models
1.1 Structure of the Book
This book is split into a few core components covering fundamental concepts:
- Chapter 1 motivates the need to consider heavy-tailed loss process models in operational risk (OpRisk) and insurance modeling frameworks. It provides a basic introduction to the concept of separating the modeling of the central loss process and the tails of the loss process through splice models. It also sets out the key statistical questions one must consider studying when performing analysis and modeling of high consequence rare-event loss processes.
- Chapter 2 covers all the fundamental properties one may require in univariate loss process modeling under an extreme value theory (EVT) approach. Of importance is the detailed discussion on the associated statistical assumptions that must be made regarding the properties of any data utilized in model estimation when working with EVT models. This chapter provides a relatively advanced coverage of generalized extreme value (GEV) family of models, block maximum and peaks over threshold frameworks. It provides detailed discussion on statistical estimation that should be utilized in practice for such models and how one may adapt such methods to small sample settings that may arise in OpRisk settings. In the process, the chapter details clearly how to construct several loss distributional approach models based on EVT analysis. It then concludes with results of EVT in the context of compound ...