数据挖掘方法在传统预测模型中的应用

数学建模领域中,对于解决不同类型的预测问题有一些经典的预测模型。最近日益流行的数据挖掘技术也有一些针对解决预测问题的独特的数学模型和建模方法。在此对使用传统解析式模型的预测方法与应用数据挖掘技术的数据库模型的预测方法进行了对比,重点分析了2种方法在影响因素的确定、数据规律的寻找方法以及模型侧重点选择上的不同之处,并简单讨论了如何结合2种模型的优点,将数据挖掘技术应用于传统解析式模型的建模过程之中,对已有的解析式预测模型进行改进,进而得出更加可靠准确的预测结果。     

消费行为的模糊数学模型

在购物指标体系的基础上,利用模糊数学原理,建立消费者购物的数学模型,并编出模型的计算机程序和软件,使购物者能在计算机上自行操作,以便科学、合理、有比较的选择自己所购物品,满足消费心理需求。     

浅谈高等数学教学与学生能力培养

高等教育的主要任务是培养具有创新精神和实践能力的复合型人才,而由于高等数学在不同学科、不同专业领域中所具有的通用性和基础性,使之在高校的课程体系中占有十分特殊的地位。在高等数学教学中,应重视数学思想方法的传导,加强知识过程的教学,渗透数学建模思想,并不断改革教学方法和教学手段,以达到在高等数学教学中培养学生的创新能力和实践能力的目的。     

加强和改进数学建模培训研究

数学建模培训是大学生数学建模竞赛的重要组成部分。应通过合理安排培训知识体系,优化组队方式,加大培训宣传,鼓励学生参训等,提高数学建模培训的效果。     

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.     

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.     

MaxVaR for non-normal and heteroskedastic returns¶

In this work we propose Monte Carlo simulation models for dynamically computing MaxVaR for a financial return series. This dynamic MaxVaR takes into account the time-varying volatility as well as non-normality of returns or innovations. We apply this methodology to five stock market indices. To validate the proposed methods we compute the number of MaxVaR violations and compare them with the expected number. We also compute the MaxVaR-to-VaR ratio and find that, on average, dynamic MaxVaR exceeds dynamic VaR by 5–7% at the 1% significance level, and by 12–14% at the 5% significance level for the selected indices.     

Communication costs in the performance of unrelated tasks: Continuum models and finite models

We consider two two‐person organizations, called A and B. Each organization faces a changing environment; an environment has two components and each of them is privately observed by one of the organization's two members. Each organization's task is to respond to the current environment by taking a correct action; the correct action is a known function of the environment. However, the task of A is totally unrelated to the task of B: if A knew B's current environment and B's current correct action, that would tell A nothing at all about its own current correct action (and vice versa). Now suppose that each organization performs its task by a sequence of message announcements that stop when an “action‐taker”; has just enough information about the two members’ private observations so that he can take the correct action. Suppose we measure the effort this requires by the size of the set of possible message announcements. Then a compelling conjecture says that there can be no saving in total effort if we merge the two organizations into a single four‐person organization in which a single action‐taker takes both actions.

The conjecture turns out to be true when the possible messages form a continuum whose size is measured by its dimension, provided the message‐announcing procedure obeys suitable regularity conditions. When we turn to a model in which the number of possible messages is finite, the situation is different. While a certain general proposition about coverings and projections is the main tool in proving the “continuum”; conjecture, the finite analog of that proposition is (surprisingly) false. The finite version of the conjecture holds, on the other hand, when one adds a certain regularity requirement ("contiguity") to the message‐announcement procedure. The truth of the finite conjecture without such a requirement remains open.     

Education par excellence: Developing personal competencies and character through philanthropy-based education

This teaching note presents an innovation in accounting education called the Philanthropy Project. ² The Philanthropy Project emphasizes experiential learning and is designed to promote the learning of discipline-specific concepts while simultaneously addressing the social needs of the surrounding community. In the Philanthropy Project, students receive money to distribute to not-for-profit organizations (NFPs) based on a competitive proposal process they help to develop and administer. A distinguishing characteristic of this project is that it is not a simulation. Students make real decisions that have immediate consequences to certain groups of people in their own communities. They have to make difficult choices by allocating scarce resources to some agencies and saying “no” to other agencies, all with worthy causes.