浅谈大众数学思想下的微积分教学改革

“大众数学”的口号自１９８４年提出逐渐广为人知,流传至今,几乎已成为数学教育界广泛认同的行动纲领。在大众数学思想下的微积分教学须从教材、教学手段、考试方式等方面进行改革     

对经管类学生学习微积分状况的调查研究

《微积分》是财经类院校经济管理类专业的一门专业基础课程,它的学习直接影响到其他后续数学课程和专业课程的学习,也关系到学生以后考研或深造的成绩,但是部分学生对其学习兴趣并不浓厚。本文对经管类学生学习微积分的状况进行了调查,总结了影响《微积分》教学质量的各种因素,并提出了一些提高教学质量的想法。     

Study on the evolutionary optimisation of the topology of network control systems

Computer networks have been very popular in enterprise applications. However, optimisation of network designs that allows networks to be used more efficiently in industrial environment and enterprise applications remains an interesting research topic. This article mainly discusses the topology optimisation theory and methods of the network control system based on switched Ethernet in an industrial context. Factors that affect the real-time performance of the industrial control network are presented in detail, and optimisation criteria with their internal relations are analysed. After the definition of performance parameters, the normalised indices for the evaluation of the topology optimisation are proposed. The topology optimisation problem is formulated as a multi-objective optimisation problem and the evolutionary algorithm is applied to solve it. Special communication characteristics of the industrial control network are considered in the optimisation process. In respect to the evolutionary algorithm design, an improved arena algorithm is proposed for the construction of the non-dominated set of the population. In addition, for the evaluation of individuals, the integrated use of the dominative relation method and the objective function combination method, for reducing the computational cost of the algorithm, are given. Simulation tests show that the performance of the proposed algorithm is preferable and superior compared to other algorithms. The final solution greatly improves the following indices: traffic localisation, traffic balance and utilisation rate balance of switches. In addition, a new performance index with its estimation process is proposed.     

Dynamics of solvency risk in life insurance liabilities

We describe the time dynamics of the solvency level of life insurance contracts by representing the solvency level and the underlying risk sources as the solution of a forward–backward system. This leads to an additive decomposition of the total solvency level with respect to time and different risk sources. The decomposition turns out to be an intuitive tool to study risk sensitivities. We study the forward–backward system and discuss two methods to obtain explicit representations: via linear partial differential equations and via a Monte Carlo method based on Malliavin calculus.     

数形结合法在《微积分初步》授课中的部分运用

鉴于《微积分学初步》是中央电大统设科目(学生需要参加统考),而我校相当一部分在读高职的学生数学基础知识薄弱,概念模糊,对常用公式、定理、性质记得不清,对基础知识、基本技能和基本方法掌握得不够。针对这些情况,为使复杂问题简单化、抽象问题具体化,以提高学生统考合格率,笔者在平时的授课中力求数与形的结合,并把其中的一些具体做法罗列出来,期望能起抛砖引玉之效。     

构造法在微积分中的应用研究

构造法是把数学问题进行转化来解决问题,构造的对象数学形式有方程、函数、过程、图形、命题,或是一种模式。本文对构造法在微积分中的应用进行了研究,以深化构造法在数学中的应用。     

GREEKS FORMULAS FOR AN ASSET PRICE MODEL WITH GAMMA PROCESSES

Greeks formulas of Delta, Rho, Vega, and Gamma are derived in closed form for asset price dynamics described by gamma processes and Brownian motions time‐changed by a gamma process. The model considered here includes many well‐known models of practical interest, such as the variance gamma model and the Black–Scholes model. Our approach is based upon the Malliavin calculus for jump processes by making full use of a scaling property of gamma processes with respect to the Girsanov transform. The existence of their variance is investigated. Numerical results are provided to illustrate that the derived Greeks formulas have faster rate of convergence relative to the finite difference method.     

Explicit characterizations of financial prices with history-dependent utility

The present paper demonstrates how explicit representations of financial prices and returns can be derived in economies with history-dependent utility. While the techniques are applicable to a wide range of economies, they are applied to a representative consumer economy where (i) the consumer’s preferences exhibit habit formation, and (ii) purchases of the consumption good also gives rise to a flow of services. Solutions are computed for the case of multiplicative or nonlinear habit formation, and additive service flows. Other applications are also indicated.     

Modeling of the national economies in state-space: A fractional calculus approach

A new approach to macroeconomic modeling is presented and illustrated by an application to modeling the behavior of national economies of the three Commonwealth countries. The developed approach is based on three essential modern tools.     

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.