本学术专著以分形统计分析与反馈交易策略为研究主题，旨在利用分形统计分析方法，构建反馈交易策略，探究相关应用问题；既发展了研究主题，也丰富了研究视角，还改进了研究方法；既有助于完善量化投资和金融决策理论，也有助于促进物理金融和行为金融的交叉协同，还有助于为理论研究者和实务工作者提供参考；具有重要的理论价值和深远的现实意义。

吴栩，男，汉族，博士，现为成都理工大学商学院副教授。长期从事证券投资与分形市场分析方向的研究，在《管理评论》、《系统工程》、《数理统计与管理》、Fractals、Nonlinear，Dynamics等国家自然科学基金委管理科学学部认定的重要期刊、CSSCI来源期刊、SCI检索期刊等发表学术论文20余篇，主持1项教育部人文社科青年基金项目和1项四川省科技计划软科学项目。

1 Introduction
1.1 Core research question
1.2 Explicate key concepts
1.3 Research significance
1.4 Main research contents
1.5 Structure arrangement
2 Fractal Statistics and Fractal Markets
2.1 Mathematical basis of fractal statistics
2.1.1 Mathematical basis of fractal theory
2.1.2 From fractal theory to fractal statistics
2.2 Fractal series and fractal distribution
2.2.1 Fractal time series and fractal correlations
2.2.2 Fractal distribution and statistical measures
2.3 Evolution of fractal market theory
2.3.1 Background and content of fractal market theory
2.3.2 From monofraetal market to muhifraetal market
2.4 Empirical test of muhifractal market
2.4.1 Test methods of muhifraetal market
2.4.2 Test results of muhifractal market
2.5 Brief summary and necessary explanations
3 Feedback Trading in Fraetal Markets
3.1 Empirically tested of feedback trading
3.1.1 Measurement methods of feedback trading
3.1.2 Test outcomes of feedback trading behavior
3.2 Impact of feedback trading on volatility
3.2.1 Illusions in empirical study and intuition
3.2.2 True facts under fractal market hypothesis
3.3 Multifraetal market and feedback trading
3.3.1 Intrinsic consistency of market and trading
3.3.2 Inner necessity of fraetal market and trading
3.4 Optimal stop times and portfolio problems
3.4.1 Optimal stop times of feedback trading strategies
3.4.2 Portfolio optimization of feedback trading strategies
3.5 Brief summary and necessary explanations
4 Distributed Fraetal Feedback Trading Strategies
4.1 Study frame of distributed fraetal feedback trading strategies
4.2 Feedback trading strategies under left tail fraetal distribution
4.2.1 Theory model building under left tail fractal distribution
4.2.2 Validity of theory model under left tail fractal distribution
4.3 Feedback trading strategies under right tail fractal distribution
4.3.1 Theory model building under right tail fractal distribution
4.3.2 Validity of theory model under right tail fractal distribution
4.4 Feedback trading strategies under fractal distribution of yields
4.4.1 Theory model building under fractal distribution of yields
4.4.2 Validity of theory model under fractal distribution of yields
4.5 Brief summary and necessary explanations
5 Correlated Fraetal Feedback Trading Strategies
5.1 Study frame of correlated fractal feedback trading strategies
5.2 Feedback trading strategies based on monofractal correlation
5.2.1 Theory model building based on monofractal correlation
5.2.2 Validity of theory model based on monofraetal correlation
5.3 Feedback trading strategies based on muhifractal correlation
5.3.1 Theory model building based on muhifractal correlation
5.3.2 Validity of theory model based on multifractal correlation
5.4 Brief summary and necessary explanations
6 Fractal Adaptive Feedback Trading Strategies
6.1 Stop times and fractal adaptive feedback trading strategies
6.2 Optimal stop times of adaptive feedback trading strategies
6.3 Brief summary and necessary explanations
7 Research Conclusions and Research Expectations
7.1 Research conclusions
7.2 Research expectations
Main References