New majorization theory in economics and martingale convergence results in econometrics

The dissertation provides a unified approach to the study of a number of important problems in economic theory, mathematical finance and econometrics using new majorization theory and martingale convergence methods. The dissertation has three chapters. The first chapter develops a unified approach to the analysis of several models in economics that depend on the majorization properties of convolutions of distributions. The main results show that many economic models are robust to heavy-tailedness assumptions as long as the distributions entering these assumptions are not too thick-tailed. But the implications of these models are reversed for distributions with very long-tailed densities. The second chapter of the dissertation presents applications of the new majorization theory developed in Chapter 1 to the study of properties of inheritance models that have been a subject of an increasing interest in economics in recent years and analyzes robustness of these models to heavy-tailedness of traits. The third chapter of the dissertation is a joint work with Peter C. B. Phillips. It presents a new and conceptually simple method for obtaining weak convergence of partial sums and multilinear forms to stochastic integrals, thereby providing for the first time a completely unified treatment of the asymptotics for stationary autoregression and autoregression with roots at or near unity.