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

Agent-based Models with Stochastic Differential Equations in Systems Biology and Financial Economics

王澤毅(Tse-Yi Wang)

指導教授 ： 高成炎

國立臺灣大學/電機資訊學院/資訊工程學研究所/博士(2009年)

https://doi.org/10.6342/NTU.2009.00771

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

agent-based models ； stochastic differential equations ； complex systems ； randomness ； emergence ； statistical physics ； gene regulatory networks ； stock markets

參考文獻

1. Abbott, R.G. et al. (2006) Simulating the hallmarks of cancer. Artif. Life, 12, 617-634.

2. Akaike, H. (1974) A new look at the statistical model identification. IEEE Trans. Automat. Control, AC-19, 716-723.

3. Anderson, P.W. (1972) More is different. Science, 177, 393-396.

4. Arifovic, J. (1994) Genetic algorithm learning and the cobweb model. J. Econ. Dyn. Control, 18, 3-28.

5. Arthur, W.B. (1999) Complexity and the economy. Science, 284, 107-109.