Uma introdução a grandes desvios com aplicações em finanças quantitativa

Abstract

In this dissertation we will introduce the reader to The Theory of Large Deviations. We will develop results that will allow us to estimate the decay rate of the probability of an event, as well as an introduction to an application in quantitative finance. The main results of this work are Sanov’s Theorem, which allows us to study the decay speed of probabilities in a finite set, Crámer’s Theorem, which allows us to study the decay speed of probabilities in R, and a Theorem in the Sanov’s Theorem, which introduces us to the study of Losses in Large Risk Credit Portfolios.