計畫中嘗試以列蒙地卡羅抽樣法作為基礎，推出一套廣泛能適用於適應性監測投資組合管理，同時能夠從海量數據中歸納資訊並在可掌控、容易更新、管理的資產配置中維持良好的績效。在計畫中我們一反過去投資組合建構先估計再最適化的作為，反向思考地先從大量可得的資產中以符合虛無範數條件下的迴歸變數選擇問題為憑藉，優化找出一組相對為數較小的資產個數開展我們的投資組合；再接續為這些為度較低的資產報酬建構較一般性、容許較多建模彈性地的狀態空間動態模型供後續監控、調整。計畫中我們嘗試納入新的基因演算法提升求解的效率並與序列蒙地卡羅法，以及其他相關做法進行比較。我們也將相關的方法應用到指數型基金的績效追蹤、以及時間序列中結構改變點的認定等問題中，並進行相關的比較。最末，我們回到利用所選的資產組合標的配適一般化動態系統的估計、推論、學習與比較，以便日後資訊的更新與調整。我們相信這樣的分析方法工具與架構將有助於許多經濟與財金領域相關模型的估計。 ;We propose a comprehensive modelling approach based on sequential Monte Carlo to adaptively monitor portfolio management and enable deduce information from massive data set yet maintain superior performance with an easy-to-update and manageable portfolio allocation and manage system. Set against the classical first-inference-then-optimize procedure, we begin with a reverse engineering by firstly propose to select only a handful of small number of assets and optimal weights with sparsity from a big sky of assets using newly developed variable selection under a penalized zero-norm constraint. The chosen assets are then modeled and estimated with a general state-space model in a concise way. We introduce and examine the performance of a stochastic genetic differential algorithm in our application. The proposed alternative approaches are then applied in the context of portfolio selection/index tracking/identification of structural breaks. We then build a general state-space model with flexible specifications for the chosen assets for dynamic modelling, and adaptive monitoring and updating. We believe this analyzing framework based on SMC may shed lights on future modelling, and effective updating for applications in Economic and Finance.
