In this third chapter on dependence modelling in OpRisk, we utilise the theory and models developed in the previous two chapters to construct a range of OpRisk LDA models that are directly applicable to practitioners. These include:
- Multiple risk LDA compound Poisson processes and Levy copulas;
- Multiple risk LDA models with dependence between frequencies via copula;
- Multipel risk LDA models with dependence between event times via copula;
- Multiple risk LDA models with dependence between severities via copula;
- Multiple risk LDA models with common shock process dependence features and self chaining copula models;
- Multiple risk LDA models with dependence between annual (aggregate) losses via copula.; and
- Multiple risk LDA models with dependence in the risk profiles of the LDA model frequency and severity parameters.
We then conclude the chapter with a complete model of multiple risk LDA models with multiple data sources combined and dependence structures incorporated. We demonstrate the properties of such a model and show how to make inference with this model under a Bayesian formulation with MCMC samplers via a Slice sampler. A numerical example is developed and the predictive posterior distribution specified.
12.1 Multiple Risk LDA Compound Poisson Processes and Lévy Copula
Characterizing multivariate Lévy processes has been an active topic in recent years for financial mathematics, risk, and insurance. In general, there are ...