策略理論

Abstract

在本論文中，我們提出策略理論，對策略的抽象概念直接做定義並且對策略理論 做了正規的數學分析。我們把策略當作一個代數空間，討論其中可以進行的基本代數 操作，並提出嚴謹的產生，組合，與最佳化策略的方式。我們用台灣期貨的資料做測 試，以展現我們的理論的可行性，並且驗證策略空間中的代數操作的確會產生預期中 的效果。

我們試圖對決策問題提出一個抽象而且普適性的數學理論，希望藉此避免掉許多既 有決策理論所需要的前提、假設、與限制(而這些前提假設在財務資料裡面的確常常不 符合)。藉由這個抽象的架構，我們提出一個穩健的線上學習系統，可以快速的適應統 計模型的改變，也對於異常現象可以有適當的反應，並且為許多既有的方法提供一個 統一的方式來做模型的篩選。有了普適性的理論之後，我們也提供一套可以直接反應 理論直覺的系統設計規範。並且用台灣期貨的交易資料來證明，這樣的系統規範的確 很容易可以應用在實際的例子上，也用這個系統來實驗證明理論的可行性。

In this thesis, we give a formal mathematical analysis on the theory of strategy, and a formal way to evaluate and compare strategy. We then discuss algebraic operations on strategy and their effects, establishing a formal way to generate, combine, select, and improve strategy. We use financial time series as example, and we focus on the study of methods based on our model and show that the algebraic operation on these strategies indeed behave as predicted.

We seek to give a more abstract and general theory on strategic decision making, in hope to avoid the various constraints and assumptions needed for classical decision model (which often are not satisfied in financial data). In doing so, we have a more robust system that adapts to model change quickly, react to anomalies correctly, and we are able to bring various different models proposed in the past under an unifying context to compare, and do model selection. Since the theory is widely applicable in various disciplines, this thesis will give a prototype on the system design that reflects intuitively from the mathematical theory, which can be conveniently modified to fit your particular need. We will also test on real world data to demonstrate its strength.