科学计算及其在晶体生长研究中的应用

本文阐述了科学计算的内容、方法和意义，讨论了科学计算在晶体生长研究中的作用以及对工科数学教学的启示。     

一道高考题的思维路径分析

纵观近几年的高考试题，对有关函数与导数的综合题的考察越来越受到重视．高考对有关函数与导数的考察重在对函数与导数知识理解的准确性、深刻性以及与其他知识版块的相互联系上．然而学生遇到利用导数相关知识研究函数的极值、单调区间、不等式恒成立以及函数零点或方程根等问题时，十分茫然，不知从何下手．本文试图通过多种思维途径人手，得到不同的解答方法，从而使此类问题得到有效解决．     

学三角 感受美

三角学是研究三角函数与解三角形的数学科目，它的形成、发展以及研究对象都与图形密不可分，而讨论和研究的工具却是数、式，因此三角学本身就是数形结合的完美体现，如果我们从数学美的角度审视三角学、学习三角函数，不仅能加深对三角知识的理解，更能获得美的享受．     

货币政策不确定性对企业经营风险的影响

新冠疫情以来企业面临的经营困境不断增加，本文考察了货币政策不确定性对企业经营风险的影响效应、作用机制及其经济后果。研究发现，货币政策不确定性下降显著降低了企业的经营风险，该效应在宽松货币政策执行之后逐步增强。进一步影响机制检验表明，“融资效应”和“信贷效应”是降低企业经营风险的重要渠道，企业所获得的债务融资以及信贷配置上升，企业财务状况改善，进而缓解企业经营困境。从异质性上看，货币政策不确定性对民营和外资企业、小规模企业、制造业企业的经营风险作用效果更强。同时，本文还通过替换被解释变量、改变样本容量、改变回归方法以及进行内生性检验等方法来保持实证结果的稳健性。因此，本文丰富了货币政策不确定性对微观经济主体的影响研究。     

由2008年高考数学卷引起的思考及启示——半个多月的部分来稿综述（待续）

进入六月下旬以来，对2008年高考数学卷的讨论的文章如潮水般涌来，对高考数学题进行研究、探源、推广以及反思教学：我们应该如何进行教学才能更有效？其中精彩独到见解甚多，我们不可能一一发表，但又弃之太可惜，研究再三，决定择其要点进行一个综合报道．请没有用其材料的作者谅解：实在是篇幅所限，杂志容量有限，不可能面面俱到．     

基于损失函数的GARCH类模型波动率预测评价

本文的目的是通过利用多种损失函数评估三种GARCH模型的预测精度，找到最优的股指期货日内波动率研究预测模型。利用之前的研究结果，三个沪深300股指期货日内一分钟日内收益率被用作研究对象，对标准GARCH,eGARCH以及RealGARCH三个模型做了实证检验，并利用多种损失函数，从不同角度衡量三个波动率模型的预测精度。研究发现：Sample1样本的RealGARCH模型有最好的预测效果，而Sample2样本与Sample6样本的eGARCH模型有最好的预测精度。因此，在对沪深300股指期货日内波动率研究时，应根据其样本特征，优先选择具有能够反映非对称特征的波动率模型来刻画波动过程，对未来波动率做预测。     

增长曲线模型参数估计的加权相对效率

对增长曲线模型中参数估计的相对效率，本文提出了一种新的定义－加权相对效率，并研究了它的性质，以及在文献「４」中的两种相对效率的关系。     

关于具分形边界连通区域上的谱渐近及弱Weyl-Berry猜想

本文研究了连通分形鼓上的谱渐近，对满足“切口”条件的连通分形鼓以及一类自然连通的分形鼓，分别证明了弱Weyl－Berry猜想是成立的.     

基于生命周期和交叠世代分析的养老风险管理文献综述及其启示

随着长寿风险的加剧以及人口死亡率的降低，养老风险管理的研究逐渐受到政府和学术界的广泛关注。本文系统梳理了养老风险相关驱动因素(死亡率和长寿风险)的研究，并介绍了生命周期框架与交叠世代模型(OLG)的建模过程，还对生命周期框架和OLG模型的应用研究进行了文献综述。从文献回顾来看，当前研究存在一些不足，未来的研究应基于我国人口生存特征去研究死亡率；同时，需要从生命周期框架和OLG模型研究研究应对养老风险的稳健的投资-消费决策，并在考虑对上一代老人赡养的情形下研究寿险决策。此外，随着养老风险逐步加剧，建议政府采取改进我国的多支柱养老保险体系、进一步放开生育、延迟退休及发展养老服务业等方式应对养老风险，保证我国养老金体系的可持续发展。     

模糊综合评判在数学自主学习能力评价中的应用

在“教与学”的过程中，教学方法的探寻与评价体系的建立一直是当代教育领域研究的两个重要方面．同样，在培养学生数学自主学习能力的过程中，如何确立合适的教学方法以及合理的评价体系也是相关教育领域需要长期研究的两个重要问题．目前对学生自主学习能力的研究主要集中在教学方法的探寻方面，侧重于教师应该如何进行教学改革、     

多利率下的寿险费率测算模型

为了能够在多利率条件下测算人寿保险的费率,本文建立了一个线性规划模型.根据该模型,能够合理安排保费资金的投资期限以达到最大的保险利益,从而为费率和红利的测算提供了依据.列出了两个典型寿险产品的计算数据,结果表明,寿险费率的测算主要取决于长期利率.对于储蓄型寿险,资金的运用应该以长期投资为主,分红水平可以由长期利率与预定利率之差来确定.     

具有储蓄功能的养老保险精算模型

本文建立了一个综合养老保险精算模型 ,把几种保险产品统一在模型中 ,模型包括延期支付的年金部分 ,终身寿险部分和还本部分 ,保险公司可以根据不同的实际情况 ,调整参数 ,通过不同参数的组合 ,获得不同的养老保险产品 .还本部分的引入 ,使得这种保险产品具有储蓄的性质     

综合人寿保险精算模型

保险是金融的重要组成部分，国际保险业发展迅速，我国保险业务较晚，资料匮乏，迫切需要引进国外先进的保险经验和保险技术，并结合我国的实际情况加以运用。本文建立了一个综合的人寿保险精算模型，其中包括生存年金，终身寿险和还本部分。通过适当的调整参数进行组合，可以获得不同的保险产品。     

A general asset-liability management model for the efficient simulation of portfolios of life insurance policies

New regulations and a stronger competition have increased the importance of stochastic asset-liability management (ALM) models for insurance companies in recent years. In this paper, we propose a discrete time ALM model for the simulation of simplified balance sheets of life insurance products. The model incorporates the most important life insurance product characteristics, the surrender of contracts, a reserve-dependent bonus declaration, a dynamic asset allocation and a two-factor stochastic capital market. All terms arising in the model can be calculated recursively which allows an easy implementation and efficient simulation. Furthermore, the model is designed to have a modular organization which permits straightforward modifications and extensions to handle specific requirements. In a sensitivity analysis for sample portfolios and parameters, we investigate the impact of the most important product and management parameters on the risk exposure of the insurance company and show that the model captures the main behaviour patterns of the balance sheet development of life insurance products.     

Life insurance in a portfolio context

The ownership of life insurance may be modeled as a portfolio problem in which the return on the life insurance contract is negatively correlated with the return on a claim to future wage income. The mean-variance model developed in the paper uses such a framework to express the optimal amount of insurance in terms of two components: the expected value of the wage claim and the risk/return characteristics of the insurance contract. The model thus offers an appealing way to formulate the life insurance problem in a portfolio context. Implications of the model for the functioning of a life insurance market are examined and the existence of accidental death contracts is explained.     

A unisex stochastic mortality model to comply with EU Gender Directive

EU Gender Directive ruled out discrimination against gender in charging premium for insurance products. This prohibition prevents the use of the standard actuarial fairness principle to price life insurance products. According to current actuarial practice, unisex premiums are calculated with a simple weighting rule of the gender-specific life tables. This procedure is likely to violate portfolio fairness principles. Up to our knowledge, in the actuarial literature there is no unisex mortality model that respects the unisex fairness principle. This paper is the first attempt to fill this gap. First, we recall the notion of unisex fairness principle and the corresponding unisex fair premium. Then, we provide a unisex stochastic mortality model for the mortality intensity that is underlying the pricing of a life portfolio of females and males belonging to the same cohort. Finally, we calibrate the unisex mortality model using the unisex fairness principle. We find that the weighting coefficient between the males’ and females’ own mortalities depends mainly on the quote of portfolio relative to each gender, on the age, and on the type of insurance products. The knowledge of a proper unisex mortality model could help life insurance companies to better understanding the nature of the risk of a mixed portfolio.     

Risk-minimization for life insurance liabilities with basis risk

In this paper we study the hedging of typical life insurance payment processes in a general setting by means of the well-known risk-minimization approach. We find the optimal risk-minimizing strategy in a financial market where we allow for investments in a hedging instrument based on a longevity index, representing the systematic mortality risk. Thereby we take into account and model the basis risk that arises due to the fact that the insurance company cannot perfectly hedge its exposure by investing in a hedging instrument that is based on the longevity index, not on the insurance portfolio itself. We also provide a detailed example within the context of unit-linked life insurance products where the dependency between the index and the insurance portfolio is described by means of an affine mean-reverting diffusion process with stochastic drift.     

寿险品种优化理论模型

分析了寿险品种创新依附于寿险定价的实际情况.以个体公平的现代产品创新理念,创建独立的寿险品种创新方法体系,并利用遗传算法原理给出了寿险品种优化设计的理论模型,使复杂的寿险品种创新过程得以量化,从而变得简洁直观,并富有方便的可操作性,适合计算机并行处理.这一模型蕴涵了动态的思维方式,利用它可随时对寿险品种进行调整.     

Polynomial diffusion models for life insurance liabilities

In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model can be used to guarantee not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit formulas.     

Valuation of life insurance products under stochastic interest rates

In this paper, we introduce a consistent pricing method for life insurance products whose benefits are contingent on the level of interest rates. Since these products involve mortality as well as financial risks, we present an approach that introduces stochastic models for insurance products through stochastic interest rate models. Similar to Black et al. [Black, Fisher, Derman, Emanuel, Toy, William, 1990. A one-factor model of interest rates and its application to treasury bond options. Financ. Anal. J. 46 (January-February), 33-39], we assume that the premiums and volatilities of standard insurance products are given exogenously. We then project insurance prices to extract underlying martingale probability structures. Numerical examples on variable annuities are provided to illustrate the implementation of this method.