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This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.



Chapter 1. The Practice and Development of Digital Inclusive Finance in China

The current world is facing a new round of technological revolution and industrial revolution. New technology and new business patterns merge in endlessly. Information wave characterized by digitalized, networked, intelligentized is booming and digital economy and sharing economy develop rapid in the global scope. As one of the important content, fintech has become a hot spot in the global financial innovation. In the year of 2017 and 2018, global fintech financing kept heating up, and the scale of fintech industry was rapidly expanding. The promotion of technology to finance is no longer limited to the aspects such as channels, but has been open to the deep integration of finance and technology. In the future, fintech and digital inclusive finance will give further play to their advantages and provide more new means to address the imbalance and inadequacy in financial development.
Yong Liu, Yanhong Shen

Chapter 2. On Arbitrage-Free Pricing in Numeraire-Free Markets: With Applications to Forex and Cryptocurrency

Our work presents several mechanisms to calculate indicative prices for forex and cryptocurrency markets in terms of a numeraire. One of the mechanisms is tailored for the practitioner and is thus accompanied by analytic estimates that maximize its computational efficiency. Additionally, we discuss how to leverage the prices provided by the different mechanisms in terms of a numeraire to deduce pairwise prices between all currencies. Finally, we prove a general theorem that guarantees the inability to induce an arbitrage for all the pricing mechanisms presented.
Jonathan Mostovoy, Tomás Domínguez, Luis Seco

Chapter 3. A Survey on Deep Learning in Financial Markets

Recently, deep learning has become a frontier in the area of financial markets. In this article, we make a survey on the applications about it. Firstly, we review the deep learning models, which are convolutional neural networks, recurrent neural networks, and deep belief networks. Secondly, we summarize the applications of the three deep learning models in financial markets. The applications focus on financial predictions and quantitative trading, such as sentiment prediction, index prediction, intraday data prediction, financial distress prediction, and event prediction. The applications of markets focus on stock markets, futures markets, exchange rate markets, and energy markets. Finally, there are also some innovative methods in deep reinforcement learning for applications in financial fields.
Junhuan Zhang, Jinrui Zhai, Huibo Wang

Chapter 4. Information Transition in Trading and Its Effect on Market Efficiency: An Entropy Approach

The Efficient Market Hypothesis has been well explored in terms of daily responses to market movements and financial reports. However, there is lack of evidence about information efficiency after the popularization of intraday trading. We investigate the time series properties of information adopted in the intraday market, in particular the causality effects. We use 30-min market price and news data to represent the past market data and the public information respectively, so that our analysis is in line with the EMH framework. Traders’ responses to such information are associated with the financial crisis. There was strong overreaction to market data right before the 2008 crisis and traders tend to rely more on news data during the crisis. We confirm that, in terms of the intraday information efficiency, it is worthwhile to adopt both types of information. Furthermore, there is still room for improving the price discovery process to reveal such information more effectively.
Anqi Liu, Jing Chen, Steve Y. Yang, Alan G. Hawkes

Chapter 5. Survey of Lattice-Based Group Signature

Group signature has two basic properties: anonymity and traceability. Due to its good properties, it has many applications in economy, politics, electronic voting, privacy protection, anonymous authentication and so on. But traditional group signature could not resist the quantum computational attacks. Lattice theory is seen as the most promising post-quantum crypto theory due to the fact that it is a kind of linear structure and that most of its operations are linear operations. Moreover, the lattice theory has better asymptotic efficiency than others do. The lattice-based group signature can not only keep its original security properties, but also resist quantum attacks, it has become a research hot spot. Therefore we think it’s necessary to sort out the achievements of lattice-based group signature in recent years. In this chapter we first simply reviewed the research progress of the traditional group signature, and then we summarized the main progress on lattice-based group signature schemes in recent years. Then we analysed the tools they used when designing signature schemes. In addition, we made a comparison about functionality and security assumptions. Finally, we put forward the further research direction and the development trend.
Lei Zhang, Zhiyong Zheng, Wei Wang

Chapter 6. Insight on Hybrid Organizational Performance: A Systematic Review

The development of the hybrid organization, especially social enterprises (SEs), is widely concerned by the world. Although abundant researches focused on hybrid strategy and performance improvement, the hybrid organizational performance evaluation has not been well defined. Moreover, review from the site of performance, especially the systematic review, remains sparse. Performance assessment is important to know the productivity of the hybrid organizations strategy and operation. Therefore the article aims to find an answer for the assessment of hybrid organizational performance and to find a path for further study. The authors utilized a systematic review approach to find the answer and possible study path for the future. After a strict literature selection procedure, 41 articles were adopted to form the research. By answering 5 research questions, the authors conclude that balance dual gaol is critical for the hybrid organization to achieve satisfying performance. However, accountability for dual performance objectives is one of the most challenges for hybrid organizational governance. The authors suggest that mathematically understanding the quality of performance is necessary for the performance assessment.
Yuting Wu, Yonghong Long

Chapter 7. The Complex Systems’ Methods in Financial Science and Technology

Financial systems are determined by the activities engaged by thousands of people, corporates, and countries, which are with different wishes or demands. The complexity is inevitable not only for financial markets but also for financial supervision and service. In this chapter, some of the methods, such as, the hierarchical structure of financial markets, multiscale analysis and causality analysis of the financial factors, and so on, are summarized. For modelling the evolution of the main financial indexes, a novel fractal structure model, which is iterated by self-interactive process with the external factors, is proposed. And the relevant methods proposed for the further analysis of financial systems are also been reviewed. Finally, from the viewpoint for the future development of financial technology, we propose some considerations that need to deal with, for example, the methods on advanced learning and intelligent automation or optimization for complex systems.
Wei Wang

Chapter 8. Estimating the Number of Fork Projects of Bitcoin Based on a Birth-Death-Immigration Process

Since the first cryptocurrency, Bitcoin, was invented in 2008, there are 105 Bitcoin fork projects in total. The number of them is still raising now. Whether it will keep increasing and what the increasing ratio is, are important and interesting questions. However there is no model to answer these question. Thus, this chapter tries to propose a population model, using a birth-death-immigration process, to estimate the number of Bitcoin fork projects.
Wei Dai

Chapter 9. Patterns Versus Spatial Heterogeneity—From a Variational Viewpoint

By a pattern we usually mean a spatially nontrivial structure and hence its antonym is spatial homogeneity. Alan Turing found that, in a reaction-diffusion system of two species, different diffusion rates can destabilize a spatially uniform state, leading to spontaneous formation of a pattern. This chapter proposes to generalize the notion of pattern to that of spatially heterogeneous environments and to build a unified theory of spontaneous emergence of patterns against spatially homogeneous or heterogeneous backgrounds.
Izumi Takagi

Chapter 10. A Summary: Quantifying the Complexity of Financial Markets Using Composite and Multivariate Multiscale Entropy

This a summary to introduce the composite multiscale entropy analysis and the multivariate multiscale entropy analysis as two new attempts to measure the overall complexity of the stock market, and the results will also be new input dimensions to measure financial risk. According to the combined results of the ensemble empirical mode decomposition and the composite multiscale entropy analysis the investment risk in the Chinese stock market may be relatively low, possibly because of the Chinese government’s supervision of the stock market. And the multivariate multiscale sample entropy is improved to quantify the complexity of multi-channel data over different time scales. Due to the expanded application of this method in the financial field, the complexity of the four ternary return sequences generated by each stock trading time in the Chinese stock market was quantified for the first time. We find that as the stock trading time increases, the complexity of the three-variable return series per hour shows a significant downward trend. As another new attempt, the complexity of the global stock market (Asia, Europe and the United States) is quantified by analyzing the multiple returns of the global stock market.
Yunfan Lu, Zhiyong Zheng

Chapter 11. Operator-Valued Dirichlet Forms and Module Operator Markov Semigroups

In this chapter, we extend the noncommutative symmetric Dirichlet forms to the operator-valued setting based on the framework of order Hilbert \(W^*\)-bimodules, and establish the Beurling-Deny criterion between operator-valued Dirichlet forms and the associated module operator Markov semigroups, which contain all of the scalar-valued Dirichlet forms previously studied on various noncommutative probability spaces as special cases. Finally, example of operator-valued Dirichlet form is given by module derivation in operator-valued free probability theory.
Lunchuan Zhang

Chapter 12. Dynamics in a Quasilinear Parabolic-Elliptic Keller-Segel System with Generalized Logistic Source and Nonlinear Secretion

In this chapter, we study dynamical properties of nonnegative solutions for the following quasilinear parabolic-elliptic Keller-Segel chemotaxis system with generalized logistic source and nonlinear secretion:
$$ {\left\{ \begin{array}{ll} u_t= \nabla \cdot (D(u)\nabla u)-\nabla \cdot (S(u)\nabla v)+f(u),&{}x\in \varOmega , t>0,\\ 0=\Delta v-v+u^\kappa ,&{}x\in \varOmega , t>0,\\ u(x,0)=u_0(x), &{}x\in \varOmega , \end{array}\right. }\qquad (*) $$
with homogeneous Neumann boundary conditions in a bounded domain \(\varOmega \subset \mathbf {R}^n(n\ge 2)\) with smooth boundary, where \(\kappa >0\) and the parameter functions D and S are smooth and, for some \(d, \chi >0, \alpha ,\beta \in \mathbf {R}\), \(D(u)\ge d u^{-\alpha }, S(u)\le \chi u^\beta \) for all \(u> 1\) and the logistic source f(u) fulfills \(f(0)\ge 0\) as well as \(f(u)\le a_0-b u^\gamma \) with \(a_0\ge 0,b>0,\gamma >1\). We first establish a boundedness principle for the chemotaxis system (\(*\)) asserting that blow-up of the solution is impossible if \(\Vert u(\cdot ,t)\Vert _{L^q(\varOmega )}\) is bounded for some \(q>\max \{\frac{n}{2}(\alpha +\beta +\kappa -1), 0\}\). Then, with the aid of this criterion, we show the uniform-in-time \(L^\infty \)-boundedness of solutions under either one of the followings:
\(\beta +\kappa <\max \{\gamma ,1+\frac{2}{n}-\alpha \}\),
\(\beta +\kappa =\gamma \) and \( b>b_*= {\left\{ \begin{array}{ll} \frac{[n(\alpha +\gamma -1)-2]}{n(\alpha +\gamma -1)+2(\beta -1)} \chi &{}\text { for } \beta > 0,\\ \chi &{} \text { for } \beta \le 0, \end{array}\right. } \)
\(\beta >0\), \(\beta +\kappa =\gamma \), \(b=b_*\) and either \(a_0=0\) or
$$ {\left\{ \begin{array}{ll} \ \ \ \ \ \ \ \ \ \ \ \alpha \le 1 &{} \text { for } \gamma>1,\\ \ \ \ \ \ \ 1<\alpha \le \frac{1}{2}+\frac{2}{n} &{} \text { for } 1-\alpha +\frac{2}{n+2-n\alpha }<\gamma \le 1-\alpha +\frac{4}{n}, \\ \frac{1}{2}+\frac{2}{n}<\alpha <1+\frac{2}{n}&{} \text { for } \gamma >1-\alpha +\frac{4}{n}, \end{array}\right. } $$
\(\beta =0\), \(\kappa =\gamma >1\), \(b=b_*=\chi \) and either \(a_0=0\) or \(\alpha <1+\frac{2}{n}\).
Our results capture the effects of the net proliferation rate (whether \(a_0=0\) or not) of cells and weak chemotaxis (\(\beta \le 0\)) and, they encompass and extend the existing boundedness results, and hence enlarge the parameter range of boundedness. Finally, for the prototypical choices \(D(u)=(u+1)^{-\alpha }, S(u)=\chi u(u+1)^{\beta -1}\) for \(\beta <1\) or \(S(u)=\chi u^\beta \) for \(\beta \ge 1\) and \(f(u)=au-bu^\gamma \) for some \(a\in \mathbb {R}, b>0\), the global stabilities of the equilibria \(((a/b)^{\frac{1}{\gamma -1}}, (a/b)^{\frac{\kappa }{\gamma -1}})\) and (0, 0) are investigated in great detail and their respective convergence rates are explicitly calculated out. These stabilization results exhibit the effect of each ingredient in (\(*\)) and, in particular, illustrate that no pattern formation can arise for small chemosensitivity \(\chi \) or large damping b.
Xin Wang, Tian Xiang, Nina Zhang

Chapter 13. Li-Yau Gradient Estimate on Graphs

In this chapter, we review some of the discrete notions of Ricci curvature, and summarize our research on Li-Yau gradient estimate and its applications for graphs.
Yong Lin, Shuang Liu

Chapter 14. Iterative Learning Control for FinTech

Iterative Learning Control (ILC) is a control approach for intricate systems running in repetitive tracking mode. It was firstly introduced by Uchiyama, dated back to 1978 [1], which was not widely spread because it is written in Japanese. In 1984, the paper published by Arimoto et al. [2] has attracted attention from the control community. Since then, related research of ILC have increased rapidly. Especially in the first decade of this century, ILC garnered significant developments in both theoretical and engineering aspects.
Kun Zeng


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