Chapter Sixteen Multifactor Modeling and Regression for Loss Processes

In this chapter, we introduce several statistical approaches that may be developed to incorporate Key Risk Indicators (KRIs) into a Loss Distribution Approach (LDA) model structure to add information that will inform parameter estimation and capital measurement. In particular, we demonstrate how one may introduce covariates that will allow one to model capital dynamically and the changes that may occur in capital due to risk factors that may be internal to an organization or external such as macroeconomic and microeconomic factors. We start this chapter with a basic introduction to Generalized Linear Models (GLMs), then introduce regularization concepts and quantile regression. Following this background review, we explain how to use such statistical models in practical OpRisk settings.

16.1 Generalized Linear Model Regressions and the Exponential Family

In this section, we introduce to OpRisk modelling the widely utilized class of regression models known as the GLM structure (see Nelder and Wedderburn 1972) and its hierarchical versions Lee and Nelder (1996). Effectively, the GLM is a flexible generalization of ordinary linear regression that allows for response variables that are distributed from a more general distribution than the standard linear model, which assumes normally distributed responses. Throughout this chapter we will develop a general framework for the introduction of such regression ...

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