應用高效率隨機規劃演算法於多期動態資產配置最佳化的研究

近年來投資理財一直深為人們所重視，因每個人都想以錢滾錢，因此該如何達到投入資產配置最佳化就是一個很重要的研究領域。本研究利用隨機規劃法來模擬資產配置，找出適合投資人之配置比例。於期初投入一筆資金利用每季動態調整各項資產的比例其各項資產即為決策變數且動態調整各變數比例值，以計算出期末預期報酬。但由於多個決策變數且需要大量計算，雖然電腦可以求算出最佳解，但若耗時過久，無法在有限合理的時間求出合理的解亦是枉然。如果想節省時間，過度減化其演算法的搜尋過程，可能會發生無法找到理想的最佳解。如何在效率及正確性上求得平衡點，是一重要課題。本研究結合MPI平行運算機制以縮短整個運算時間和提昇其時效性，並將期末求解的預期報酬與各種傳統的資產配置策略做比較，包括買入持有策略(Buy-and-Hold)、固定比例策略(Constant Mix)、固定比例投資組合策略(Constant Proportion Portfolio Insurance)及時間不變性投資組合策略(Time-Invariant Portfolio Protection)來驗證隨機規劃是可以優於過去的方法。

關鍵字

動態資產配置；平行計算； MPI ；隨機規劃法

並列摘要

Financial investing has become a very popular topic because people hope to expand their wealth by proper investing. Thus, how to reach the optimal asset allocation has been an important research area. This study adopts the “stochastic programming” technology to simulate the assets allocation and then find the optimal asset ratios. In this study, certain amount of capitals is initiated and distributed to different assets and changes the combination ratios every season to reach the largest financial outcome. Those dynamically changed asset ratios are the determining variables for the financial model. Since the model used in this study has lot of determining variables, it consumes huge computational resources. Even though the current computer can solve for solution, yet it becomes impracticable if it takes unreasonable computation time. One might simplify the financial model to reduce the calculation requirements, however, too much simplification could cause the algorithm converge to local optimal. Thus, how to obtain good balance between efficiency and accuracy has been a tough question. In order to handle this dilemma, this study embeds the parallel computation using “Message Passing Interface” (MPI) to shorten the entire simulation period and increase the efficiency without losing the accuracy. The final simulated optimal solutions are compared with four traditional investing strategies – such as the “Buy-and-Hold”, “Constant Mix”, “Constant Proportion Portfolio Insurance” and “Time-Invariant Portfolio Protection”. The results show that the financial outcomes from simulated optimization are superior to those from traditional investing strategies.