The Archimedean Connection Function And Its Application In Portfolio Optimization

Copula are functions that join or "copula" multivariate distribution functions to their one-dimensional marginal distribution functions.Given a Copula and the onedimensional marginal distribution functions,we can construct the join multivariate distribution.Because of this,using Copula can construct a lot of join distributions, such that we can drop the joint normality assumption on returns.This dissertation consists of four chapters.Chapter one is the preface,we introduce the measure of risk—Conditional Value-at-Risk(CVaR) and its use in optimizing portfolio;The use of copula in optimizing portfolio and introduced the optimizing model of portfolio we proposed based on Archimedean.In Chapter two,we introduce the Copula,such as its definition,properties,estimation and simulation,especially Multivariate Archimedean's definition,properties, Geometrically Designed Spline(GeDS) estimation and simulation.At last we introduce a method to construct Copula—Pair-Copula construction(PCC).In Chapter three,we proposed a method to estimate and simulate PCC-Archimedean Copula which is based on the estimation and simulation of Archimedean Copula.Then we proposed the procedure of portfolio optimization based on PCC-Archimedean Copula or multivariate Archimedean Copula.At last,we discussed the comparison of the model of portfolio optimization.In the last Chapter,we apply the three-dimensional Archimedean Copula and three-dimensional PCC-Archimedean Copula in the empirical study.Use the method we proposed in chapter three to optimizing portfolio.Empirical study demonstrate that the multi-Archimedean Copula and multi-dimensional PCC-Archimedean Copula based CVaR method does better in the optimizing of portfolio than t-Copula and Clayton Copula.