基于加权可能性均值的亚式期权模糊定价

主要探讨不确定环境下用模糊集理论处理亚式期权的定价问题.运用梯形模糊数来表示标的资产价格、无风险利率、红利率和波动率,建立了亚式期权的加权可能性均值模糊定价模型,得到连续几何和算术亚式期权的模糊价格公式.最后通过数值例子表明:亚式期权的加权可能性均值模糊定价模型具有很大的灵活性,更符合现实的不确定情况,具有较强的实用价值.     

An algebraic translation task solved by grade 7–9 students

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school year. Among students who could solve the arithmetic part of the problem, the use of variables in the correct conventional notation appeared from grade 7 and continuously increased through grade 9. These results suggest that there is a relationship between students’ arithmetic understanding and translating verbal problems into algebraic statements relating two variables.     

A cycle for validating a learning progression illustrated with an example from the concept of function

A learning progression, or learning trajectory, describes the evolution of student thinking from early conceptions to the target understanding within a particular domain. As a complex theory of development, it requires conceptual and empirical support. In earlier work, we proposed a cycle for the validation of a learning progression with four steps: 1) Theory Development, 2) Examination of Empirical Recovery, 3) Comparison to Competing Models, and 4) Evaluation of Instructional Efficacy. A group of experts met to discuss the application of learning sciences to the design, use, and validation of classroom assessment. Learning progressions, learning trajectories, and how they can support classroom assessment were the main focuses. Revisions to the cycle were suggested. We describe the adapted cycle and illustrate how the first third of it has been applied towards the validation of a learning progression for the concept of function.     

Connecting multiplicative thinking and mathematical reasoning in the middle years

Mathematical reasoning and problem solving are recognised as essential 21st century skills. However, international assessments of mathematical literacy suggest these are areas of difficulty for many students. Evidenced-based learning trajectories that identify the key ideas and strategies needed to teach mathematics for understanding and support these important capacities over time are needed to support teachers and curriculum developers so that they do not have to rely solely on mathematics content knowledge. Given this goal and recent evidence to suggest a relationship between the development of multiplicative thinking and mathematical reasoning, this paper explores the processes involved in developing a single, integrated scale for multiplicative thinking and mathematical reasoning using data from a four-year design-based project to establish learning and assessment frameworks for algebraic, geometrical and statistical reasoning in the middle years of schooling.     

Minimizing convex quadratics with variable precision conjugate gradients

We investigate the method of conjugate gradients, exploiting inaccurate matrix‐vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring in the theoretical bounds estimated, leading to a practical algorithm. Numerical experiments suggest that this approach has significant potential, including in the steadily more important context of multiprecision computations.     

关于广义Euler多项式和分式的讨论

This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally, a short proof of a certain summation formula is given.     

Undecidability of the Real-Algebraic Structure of Scott's Model

We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows.     

区间数的标准表示及其四则运算法则与泛灰数的内在联系

在回顾泛灰数四则运算法则基础上,给出了区间数的标准表示,论述了标准区间数的四则运算法则与泛灰数的内在联系及其应用前景.     

一元非线性系统的BP算法研究

详细研究了一种一元非线性系统的BP算法,提出并证明了该算法的收敛性定理,给出了该算法的应用实例.计算机仿真结果表明:对于随机给定的初始点,该算法都能稳定收敛到它的一个实根,而且计算精度可控,因此,该算法是有效的.与传统的计算方法相比,本文算法不仅具有收敛速度快,而且计算精度可控以及初始点随机给定的集中优点.