臺灣博碩士論文加值系統

我們以寡勝賽局的概念建構了虛擬的市場，討論寡勝玩家群體在開放系統與非開放系統兩種不同環境下的獲利機率分佈圖。我們也比較了在市場充滿了寡勝玩家的情況下，當沖客與寡勝玩家獲利的機率。結果顯示，在開放系統中，若市場價格穩定且皆由寡勝玩家所決定，平均而言玩家們將會虧損，但若市場呈現多頭或空頭的格局，即離場價格與入場價格差距較大時，平均而言玩家們將會獲利。為了進一步分析實際上當沖客在寡勝玩家所組成的市場中獲利的情況，我們建議在賽局中加入經濟情況的時間相關性，使當沖客和市場之交互作用更加真實。

We construct an artificial market based on the minority game (MG). We then compute the profit probability distributions of the MG group in an open system or a close system. We also compare the profit probability distributions between a day trader and an MG trader in a market composed of MG traders. In an open system, if the price is fluctuating and totally determined by MG traders, the average wealth of MG traders decreases. However, in the bear or bull market, i.e. when the difference between the first and final price is large, the average wealth of these MG traders increases. Finally, we analyze the profit distribution of a day trader in the steady market composed of MG traders both in an open system and a close system. It is suggested that including a time-correlated information in the model will make the interaction between a day trader and the market more realistic.

誌謝 i
中文摘要 iii
ABSTRACT v
目錄 vii
圖次目錄 ix
表次目錄 xi
Chapter 1 導論 1
Chapter 2 理論暨文獻回顧 5
2.1 寡勝賽局在金融市場的應用 5
2.2 平均系統效率 10
2.3 外生歷史紀錄及經濟情況 16
2.4 可預測性 18
2.5 開放與非開放系統 21
2.6 財富方程式 23
2.7 報酬函數 26
2.8 當沖客 28
2.9 賽局演化 29
Chapter 3 研究結果 31
3.1 不可預測相之下開放系統中寡勝市場的價格及獲利 31
3.2 不可預測相之下開放系統中當沖客及寡勝玩家在寡勝市場中的獲利 35
3.3 不可預測相之下開放系統、非開放系統中當沖客及寡勝玩家在寡勝市場獲利 37
3.4 可預測相之下開放系統中寡勝市場的價格及獲利 41
Chapter 4 結論與未來工作 47
Appendix A Mathematica 程式碼 49
Appendix B 擲硬幣極限 52
參考文獻 53

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