提前还贷及其隐含期权的分析

可提前还款的定期贷款是隐含着期权的利率衍生物，本文建立CIR利率模型下可提前还款的定期贷款的数学模型，通过离散偏微分方程，建立了模型的计算方法，讨论了随机利率对提前还贷的影响．     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

金融时间序列分析与建模

介绍了金融时间序列分析与建模的主要理论、方法,着重论述了近20多年发展起来的非平稳时间序列的建模方法及工具,指出进一步的研究方向.最后,对上证综合指数这一金融时间序列进行了实证分析.     

Predicting Bitcoin (BTC) Price in the Context of Economic Theories: A Machine Learning Approach

Bitcoin (BTC)—the first cryptocurrency—is a decentralized network used to make private, anonymous, peer-to-peer transactions worldwide, yet there are numerous issues in its pricing due to its arbitrary nature, thus limiting its use due to skepticism among businesses and households. However, there is a vast scope of machine learning approaches to predict future prices precisely. One of the major problems with previous research on BTC price predictions is that they are primarily empirical research lacking sufficient analytical support to back up the claims. Therefore, this study aims to solve the BTC price prediction problem in the context of both macroeconomic and microeconomic theories by applying new machine learning methods. Previous work, however, shows mixed evidence of the superiority of machine learning over statistical analysis and vice versa, so more research is needed. This paper applies comparative approaches, including ordinary least squares (OLS), Ensemble learning, support vector regression (SVR), and multilayer perceptron (MLP), to investigate whether the macroeconomic, microeconomic, technical, and blockchain indicators based on economic theories predict the BTC price or not. The findings point out that some technical indicators are significant short-run BTC price predictors, thus confirming the validity of technical analysis. Moreover, macroeconomic and blockchain indicators are found to be significant long-term predictors, implying that supply, demand, and cost-based pricing theories are the underlying theories of BTC price prediction. Likewise, SVR is found to be superior to other machine learning and traditional models. This research’s innovation is looking at BTC price prediction through theoretical aspects. The overall findings show that SVR is superior to other machine learning models and traditional models. This paper has several contributions. It can contribute to international finance to be used as a reference for setting asset pricing and improved investment decision-making. It also contributes to the economics of BTC price prediction by introducing its theoretical background. Moreover, as the authors still doubt whether machine learning can beat the traditional methods in BTC price prediction, this research contributes to machine learning configuration and helping developers use it as a benchmark.     

金融发展对经济增长影响的实证分析

本文将金融发展作为一个独立解释变量引入,构造经济增长的面板数据模型,运用面板数据以1994年为分界点分两阶段实证分析了全国及东、中、西部地区1985~2003年金融发展对经济增长的影响,以及东、中、西部地区影响的差异性,模型较好地拟合了数据。实证分析表明,各地区之间金融发展的不平衡性可以部分解释其经济增长的差异性。     

围绕财经特色主题加强《高等代数》精品课程建设

我校精品课程《高等代数》建设的思路是,围绕财经特色主题,坚持以高等代数理论为基础,以经济、管理类的专业为依托,以数学实验室为训练基地,将数学建模的思想融入到《高等代数》的教学活动中.这种教学模式的改变不仅有利于学生的培养,而且有助于培养出一支有较高水平的师资队伍.使我们的《高等代数》课程真正成为高水平、高质量的示范性课程.     

A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters

In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd.     

Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

基于多元分析的股票评价方法

对上市公司钢铁板块2004年财务报表中的八个主要指标应用多元分析法进行了总体评价,得出上市公司的业绩主要受三个具有一定含义的因子的影响,并对上市公司各因子的得分情况及综合得分情况给出了相应分析.