Multiple Risk Factors Dependence Structures With Applications to Actuarial Risk Management

Actuarial and financial risk management is one of the most important innovations of the 20th century, and modelling dependent risks is one of its central issues. Traditional insurance models build on the assumption of independence of risks. Criticized as one of the main causes of the recent financial crisis, this assumption has facilitated the quantification of risks for decades, but it has often lead to under-estimation of the risks and as a result under-pricing. Hence importantly, one of the prime pillars of the novel concept of Enterprise Risk Management is the requirement that insurance companies have a clear understanding of the various interconnections that exist within risk portfolios.

Modelling dependence is not an easy call. In fact, there is only one way to formulate independence, whereas the shapes of stochastic dependence are infinite. In this dissertation, we aim at developing interpretable practically and tractable technically probabilistic models of dependence that describe the adverse effects of multiple risk drivers on the risk portfolio of a generic insurer. To this end, we introduce a new class of Multiple Risk Factor (MRF) dependence structures. The MRF distributions are of importance to actuaries through their connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The new constructions are also linked to the factor models that lay in the very basis of the nowadays financial default measurement practice. Moreover, we use doubly stochastic Poisson processes to explore the class of copula functions that underlie the MRF models. Then, motivated by the asymmetric nature of these copulas, we propose and study a new notion of the paths of maximal dependence, which is consequently employed to measure tail dependence in copulas.