基於模擬之多目標投資組合最佳化風險管理

Simulation Based Multi-objective Portfolio Optimization with Risk Management

石涵琳(Han-Lin-Shih)

指導教授 ： 尹邦嚴

國立暨南國際大學/管理學院/資訊管理學系/碩士(2016年)

摘要

投資組合最佳化(Portfolio Optimization)問題，一直是相當熱門的研究議題，但考量的資產或股票數目愈多，其複雜度亦相對愈高。模擬最佳化（Simulation Optimization）技術，可以有效解決數學模型中較難處理的解析公式，以系統模擬取代解析求解，同時避免在真實環境中實際系統實作所產生之巨大成本及風險；但模擬最佳化有計算耗時及受到隨機誤差干擾的缺點，需要透過長時間的模擬計算，以提升模擬結果的精確性。演化式演算法(Evolutionary Algorithms，EAs)已被廣泛應用於求解多目標最佳化問題(Multi-objective Optimization Problem)，其中拆解式多目標演化式演算法(Multi-objective Evolutionary Algorithm Based on Decomposition, MOEA/D)為目前解決多目標最佳化問題著名的演算法之一，透過數學規劃法中拆解的概念，MOEA/D將多目標最佳化問題拆解成數個單目標子問題，並同時對數個子問題進行優化，以保持良好的適合度(Fitness)及多樣性(Diversity)。本研究採用台灣50中之46檔股票資料，以MOEA/D演算法結合模擬最佳化技術，求解在各種風險控管機制下的台股投資組合最佳化問題。本論文提供四種不同收益-風險模型，並分別探討各個模型之優劣，以提供投資者作為決策之參考依據。

關鍵字

投資組合最佳化 ； 模擬最佳化 ； 演化式演算法 ； 多目標最佳化問題 ； 拆解式多目標演化式演算法

並列摘要

Portfolio optimization is the process of choosing an optimal asset allocation in a portfolio, aiming to maximize the portfolio's expected return for a defined level of risk or minimize the portfolio's expected risk for a given level of expected return, has been receiving considerable attention from both finance professionals and academics.
Simulation Optimization is the process of finding the best values of input variables without explicitly evaluating all possibilities of input variables, its objective is to minimize the computational resources spent as well as maximizing the information obtained through simulation. The simulation model is effective as a replacement for the mathematical model of the real system to reduce costs of training. Nevertheless, Simulation Optimization still has some weaknesses such as the time consuming and the influence of random errors, it is also impossible to guarantee the result accuracy as the result can be only near global extreme.
Multi-objective optimization considers mathematical optimization problems involving more than one objective functions to be optimized simultaneously. Evolutionary Algorithms have been extensively applied to solve multi-objective optimization problems, in which Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is currently one of the most popular choices due to its high search ability as well as high computational efficiency.
The purpose of this research is to apply MOEA/D and Simulation Optimization to find the Pareto sets of portfolio optimization problems and to analyze the effect of various risk models of Simulation Optimization on the performance.

並列關鍵字

Portfolio optimization ； Simulation optimization ； Evolutionary algorithms ； Multi-objective optimization problems ； Multi-objective evolutionary algorithm based on decomposition

參考文獻

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