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研究生:王澤毅
研究生(外文):Tse-Yi Wang
論文名稱:結合代理人模型與隨機微分方程於系統生物學與財務經濟方面的應用
論文名稱(外文):Agent-based Models with Stochastic Differential Equations in Systems Biology and Financial Economics
指導教授:高成炎高成炎引用關係
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:資訊工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:108
中文關鍵詞:代理人模型隨機微分方程複雜系統隨機性浮現統計物理基因調控網絡股票市場
外文關鍵詞:agent-based modelsstochastic differential equationscomplex systemsrandomnessemergencestatistical physicsgene regulatory networksstock markets
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生物網絡與經濟體系皆為複雜隨機系統。目前針對特殊情況下之複雜性與隨機性已有的研究方法,大致可區分為兩類:一為應用統計物理模型以進行演繹邏輯推理,另一為不使用統計物理模型,但採用歸納分析來建構實質理論。在本篇論文中,我們將提出基於代理人模型與隨機微分方程而發展出的一般性之結合方法。先藉由觀察系統隨著時間改變的模式,歸納建構出用於現實預測的實質隨機微分方程,並同時定義出可執行電腦虛擬實驗的代理人模型,在我們所提出的一般性之結合方法論中,加諸於虛擬代理人行為的假設,可演繹推導出實質隨機微分方程,以描述現實世界中隨著時間變化的機制。

我們將探討兩組案例來說明此結合方法: 其一為系統生物學上基因調控網絡的模型,另一為財務經濟學中預測股價指數的波動。兩者皆顯示出結合代理人模型與隨機微分方程為複雜隨機系統提供更完整的研究方法,更堅實的連接電腦虛擬實驗與現實世界預測。
Biological networks and economic systems are complex stochastic systems. There are several particular approaches to deal with the complexity and stochasticity. But this field has become a battleground for two distinct methods: those employing statistical physics models tend to follow deductive approach, and those who do not use physics models favor inductive method of realist theory construction. In this dissertation, we propose a general combination methodology based on agent-based models, which is a variation of the statistical physics model, and stochastic differential equations. Starting with observation on the way systems change over time, the realist stochastic differential equations are inductively constructed for real-world prediction, and the artificial agent-based models are analogically simulated for in-silico experiments. The main result of this combination methodology exhibits that the artificial rules imposed on behaviors of in-silico agents deductively lead to the realist equations describing time-dependence of real-world mechanisms.

To illustrate the methodology, two case studies are presented: one is to model gene regulatory networks in systems biology and the other is to predict stock indexes in financial economics. Both examples demonstrate that combining agent-based models with stochastic differential equations provides a more complete methodology for complex stochastic systems, and establishes a more solid linkage between in-silico experiments and real-world prediction.
誌謝 I
摘要 II
Abstract III
Content IV
List of Figures VII
List of Tables VIII

Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Contributions 5
1.3 Background 7
1.3.1 Statistical Physics Models 8
1.3.2 Agent-Based Models (ABMs) 12
1.4 Realist Theory Construction 15
1.5 A General Combinative Methodology 18
1.5.1 Introduction to Stochastic Differential Equations (SDEs) 18
1.5.2 Combining ABMs with SDEs 20
Chapter 2 Realist Stochastic Differential Equations 23
2.1 Gene Regulatory Networks (GRNs) 23
2.2 Stock Market Systems 25
2.3 Realist Stochastic Differential Equations 26

Chapter 3 Agent-Based Models 29
3.1 Defining ABMs for GRNs 29
3.2 Multi-agent Systems for GRNs 31
3.2.1 Basic Behaviors of Molecular Agents 32
3.2.2 Specific Reactions between Molecular Agents 34
3.3 Notations and Restrictions for GRNs 38
3.4 Defining ABMs in Financial Economics 40
3.4.1 Modified Sugarscape 41
3.4.2 Rules of Behaviors for Economic Agents 42
Chapter 4 Complex Stochastic Differential Equations 45
4.1 Introduction 45
4.2 Dynamical State of ABMs for GRNs 46
4.2.1 Mathematical Premises of Transcription and Translation 47
4.2.2 Mathematical Premises for Biochemical System 51
4.2.3 Mathematical Premises about Binding and Regulation 53
4.2.4 Summary of Mathematic Premises in ABMs for GRNs 54
4.3 Chemical Master Equations for GRNs 55
4.4 Complex Stochastic Differential Equations for GRNs 58
4.5 Deriving Complex SDEs in Modified Sugarscape 61
Chapter 5 Implementation in Systems Biology 65
5.1 Quantifying the GRN in Saccharomyces cerevisiae 65
5.2 Reducing Complex SDEs to Realist Ones 69
5.3 Linear Regression Equations 73
5.4 Computational Forward Selection 76
5.5 Results 78

Chapter 6 Implementation in Financial Economics 82
6.1 Market Trends: Bull and Bear 82
6.2 Price Movements 85
6.3 Predicting Stock Indexes 88
Chapter 7 Conclusion 92
7.1 Summary 92
7.2 Discussions 95
7.3 Future Works 96

Bibliography 97
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