在國際間的股票市場中，股票報酬常存在有不對稱的相關結構，而其會造成許多極度地尾端風險。Copula函數常被用來描述多變數之間的聯合相關程度。多數的文獻均以二元copula函數為架構，去描述多種不同資產，像是股票、債券、匯率等之間的關係。我們討論多元copula的應用，本文以四元copula為主軸，並輔以狀態轉換 (regime-switching) 之機率過程，建構出四資產的投資組合之相關結構模型。 考慮了狀態轉換之copula的配適性後，我們以此模型來做資產投資策略。在模擬過程中，我們嘗試根據不同的未來目標做出最佳的投資組合權重，並採用動態預期模型 (dynamic anticipative model) 來藉由資訊的不斷更新，重新估計模型的參數來做資產評估。實證結果上，我們發現考慮狀態轉換之copula模型可以捕捉到更多股票報酬波動的情形，因此能減少在股市共跌時造成的重大損失。 / The correlation of returns in international stock markets exist asymmetric structure, which cause extremely tail dependence. The copula functions are commonly used to describe the dependence between random variables. Most literatures use basic pair-copulas to model the dependence of two variables, like stocks, bonds and exchange rates. This article try to use multivariate copulas, mainly 4-copula, and regime-switching method to construct a portfolio dependence, and extend to asset allocation. Given the fitting regime-switching copula, we use the model to decide investment strategy. We try to select the optimal weights of portfolio by different objective function, and we adapt a dynamic anticipative model, which can take all new information for parameters estimation. Empirically, we find that the copula-based model with regime-switching can capture more variation, and decrease the return loss from downside co-movement.

In my thesis I~ deal with the design, implementation and testing of the advanced parallel Estimation of Distribution Algorithm (EDA) utilizing copula theory to create a~ probabilistic model. A~new population is created by the process of sampling the joint distribution function, which models the current distribution of the subpopulation of promising individuals . The usage of copulas increases the efficiency of the learning process and sampling the probabilistic model. It can be separated into mutually independent marginal distributions and the copula , which represents the correlations between the variables of the solved problem. This concept initiated the usage of the parallel island architecture , in which the migration of probabilistic models belonging to individual islands ' subpopulations was used instead of the migration of individuals . The statistical tests used in the comparison of the proposed algorithm ( mCEDA = migrating Copula - based Estimation of Distribution Algorithm ) and the algorithms of other authors confirmed the effectiveness of the proposed concept .