Stock market crashes are outliers

We call attention against what seems to be a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial Average that with high probability the three largest crashes in this century are outliers. This result supports the suggestion that large crashes result from specific amplification processes that might lead to observable pre-cursory signatures. Received and Revised: 30 November 1997 / Accepted: 8 December 1997     

时域有限差分法在光波导分析中的应用及改进

对时域有限差分算法在圆柱坐标下弱导光纤中应用时吸收边界条件的设置及其对计算精度的影响进行了讨论，提出了改善的方法。并且将这种方法应用于一般光纤和光电子晶体光纤传输特性的计算，得到了有用结果。     

Shibor作为基准利率的实证研究

运用我国金融市场的实际数据,从金融市场基准利率的基本属性的角度出发对Shibor和银行间债券回购利率进行了系统地比较分析,认为Shibor虽然运行时间不长,但却具备了基准利率的主要特征.Shibor作为基准利率更具有科学性.     

Analysis of exercise boundary of American interest rate option

By applying the variational inequality technique, we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity, boundedness and C^∞-smoothness of the exercise boundary are proved in this paper.     

带利率的更新风险模型的破产概率的上界估计

本研究了在常利率条件下普通更新风险模型的破产概率问题．采用一种递推的方法给出了这种情况下破产概率的一个上界估计．     

二次型复折射率介质中的光导现象

本文讨论了n(z,r)=n_0(z)+n_2(z)r~2/r_e~2型复折射率介质中的激光传输问题,给出了激光传输参数(光束半径和波阵面曲率)的演化公式。指出只要存在一定大小的n_(21),在传输过一段特征距离z_c之后,将出现完全光导(即自相似模的传播),而且自相似模是激光体系的特征模式。其传输参数只与n_2有关,而与激光初始参数无关。自相似模必定是高斯球面波,而不是高斯平面波。     

Experimental investigation of the relativistic backward wave oscillator with a periodic guiding magnetic field

Experiment is carried out on the accelerator Sinus-700 to investigate the Relativistic Backward Wave Oscillator （RBWO） with a periodic guiding magnetic field. When the strength of the guiding magnetic field, whose period is 4.6 cm, is 0.54 T, a microwave output power of 0.95 GW at 9.1 GHz microwave frequency is achieved. It is shown that the RBWO with a periodic guiding magnetic field is feasible.     

Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

传统的保险市场难以满足日益频发的巨灾风险分散需求,巨灾债券作为一种非传统金融创新工具提供了一种新的分散机制,而精准定价则对巨灾债券的成功发行与交易起着关键作用。本文基于风险中性测度技术,在Longstaff随机利率且巨灾风险累积损失服从复合泊松损失条件下,得到了零息票巨灾债券价格公式;进一步结合广东省1989~2015年台风风暴潮灾害损失数据进行实证分析;最后,针对定价公式复杂性,本文利用快速傅里叶变换方法进行数值求解,结果验证了本文所构模型的可行性。本文的研究是希望能为我国发行巨灾债券与风险测度提供一定的理论基础与技术支持。     

The development and interaction of terrorist and fanatic groups

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to extend the theoretical framework of organizing and self-organizing social groups and communities, including terrorist groups. The main goal of our work is to gain insight into the role of recruitment and retention in the formation and survival of social organizations. Understanding the underlining mechanisms of the spread of ideologies under competition is a fundamental component of this work. Here contacts between core and non-core individuals extend beyond its physical meaning to include indirect interaction and spread of ideas through phone conversations, emails, media sources and other similar mean. This work focuses on the dynamics of formation of interest groups, either ideological, economical or ecological and thus we explore the questions such as, how do interest groups initiate and co-develop by interacting within a common environment and how do they sustain themselves? Our results show that building and maintaining the core group is essential for the existence and survival of an extreme ideology. Our research also indicates that in the absence of competitive ability (i.e., ability to take from the other core group or share prospective members) the social organization or group that is more committed to its group ideology and manages to strike the right balance between investment in recruitment and retention will prevail. Thus under no cross interaction between two social groups a single trade-off (of these efforts) can support only a single organization. The more efforts that an organization implements to recruit and retain its members the more effective it will be in transmitting the ideology to other vulnerable individuals and thus converting them to believers.     

预警信息引导条件下雷达最优搜索空域研究

提出了一种基于预警引导信息的弹道导弹防御跟踪制导雷达搜索空域最优划分模型,从搜索空域的静态划分和动态更新2个方面同时进行最优化,实现了弹道目标高速运动条件下,跟踪制导雷达对目标分布区域的连续有效覆盖,提高了雷达对目标的截获性能。最后给出了仿真结果,验证了该方法的有效性。