Stochastic Orders Applied to Insurance and Economics

Abstract

In many real-life situations, the complexity of decision-making processes is often due to the stochastic nature of the random variables involved. Stochastic Ordering Theory, which addresses the problem of the comparison between two random variables (or vectors), arises as a robust tool for decision-making under uncertainty.

In Financial Risk and Actuarial Theory, multiple risk factors interact among themselves. Hence, the intricacy of decision-making among different insurance and financial products increases manifold. In light of this fact, we must model risks considering the dependence structure of a random vector whose components are interrelated risks. Copula Theory serves as a fundamental instrument to model dependence among these components.

This Ph.D. dissertation aims to provide contributions in the scientific domain of Probability Theory, studying methodologies, based on Stochastic Orders and Copula Theory, which address a wide range of mathematical problems. In order to illustrate and highlight the applicability of the theoretical results, the present dissertation falls within the context of Financial Risk and Actuarial Theory. In line with the illustrative purpose, several examples, either based on parametric families of distributions or dealing with real-world data sets, are provided throughout the dissertation.