Optimal reinsurance and investment problem in a defaultable market

This article investigates the optimal reinsurance and investment problem involving a defaultable security. The insurer can purchase reinsurance and allocate his wealth among three financial securities: a money account, a stock, and a defaultable corporate bond. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. Using techniques of stochastic control theory, we derive the corresponding Hamilton–Jacobi–Bellman equation and decompose the original optimization problem into a predefault case and a postdefault case. Explicit expressions for optimal strategies and the corresponding value functions are derived, and the verification theorem is given. Finally, we present numerical examples to illustrate our results.     

简议二阶变系数线性微分方程解法

在理工科专业中,许多力学问题可归结为二阶微分方程,其中如何求首积分以及特解是十分重要的。许多教材对可降阶二阶微分方程,常系数线性微分方程,拉普拉斯交换解微分方程都作了比较详细的介绍,但对于二阶交系数线性微分方程的解法,没有一个定论。本文就这一问题进行探讨。     

逆序方程的解

从排列的逆序中归结出如下一个不定方程:Y_1+Y_2+…Y_(n-1)=m,0≤Y_1≤i(i=1,2,…,n-1)本文讨论了此不定方程整数解个数P_n,m的性质及计算公式。     

逻辑方程组分析及其求解方法

逻辑方程组属于逻辑代数的范畴,和线性方程组相仿,它也存在着方程的相关性和独立性以及解的组数等问题。本文先就这些问题给出初步的分析和证明;最后给出一种“降变量方程图”求解逻辑方程组的方法,并附有二例,目的在于解决逻辑方程组所含变量较多时求解困难的问题。     

几类非线性常微分方程的可积类型

本文讨论了应用广泛的几类一阶、二阶非线性常微分方程的可积类型,并给出推广的Riccuti方程初等可积的条件.文[1]—[5]是本文所得结果的特例.     

流体力学新型通用函数Ω的变分有限元分析

本文应用通用函数Ω及其变分原理,为求解具有自由面流动问题提出了一种新方法。将物理平面变换到映象平面。在映象平面上,引出通用函数Ω,并且写出关于Ω的变分原理。用这个变分原理及有限元法求解自由面流动可克服边界未知的困难。文中以水坝闸门出流问题为例进行了计算,结果表明,该方法是有效的。     

发挥小麦最适穗数在高产栽培中的优势作用

小麦最适穗数对产量的效应最大。本文应用试验资料和多项式回归方程,从数量上捕捉到以每亩24.54万穗时,籽粒产量最高。为小麦丰产栽培提供了可靠信息。     

非线性条件下的塔板理论模型和计算机模拟

以非线性吸附等温线方程Langmuir方程为例,创建了一种非线性条件下塔板理论模型的色谱流出曲线的计算机模拟方法.用此方法模拟非线性条件下的色谱流出曲线,能直观地看到吸附系数和样品量对色谱峰拖尾的影响.此模拟程序用于一些大学的色谱分析教学,效果很好.     

EXAMPLES OF MINIMUM VARIANCE ESTIMATION1

In this sequel to a previous discussion of minimum variance estimation (Bartlett, 1982), the gain with conditional estimation procedures is illustrated for the location parameter for (i) the rectangular distribution; (ii) a triangular distribution (typifying an asymmetric case). This note concludes with further remarks on the multi-sample and multi-parameter cases.     

Major Psychological Factors Affecting Acceptance of Gene-Recombination Technology

The purpose of this study was to verify the validity of a causal model that was made to predict the acceptance of gene-recombination technology. A structural equation model was used as a causal model. First of all, based on preceding studies, the factors of perceived risk, perceived benefit, and trust were set up as important psychological factors determining acceptance of gene-recombination technology in the structural equation model. An additional factor, "sense of bioethics," which I consider to be important for acceptance of biotechnology, was added to the model. Based on previous studies, trust was set up to have an indirect influence on the acceptance of gene-recombination technology through perceived risk and perceived benefit in the model. Participants were 231 undergraduate students in Japan who answered a questionnaire with a 5-point bipolar scale. The results indicated that the proposed model fits the data well, and showed that acceptance of gene-recombination technology is explained largely by four factors, that is, perceived risk, perceived benefit, trust, and sense of bioethics, whether the technology is applied to plants, animals, or human beings. However, the relative importance of the four factors was found to vary depending on whether the gene-recombination technology was applied to plants, animals, or human beings. Specifically, the factor of sense of bioethics is the most important factor in acceptance of plant gene-recombination technology and animal gene-recombination technology, and the factors of trust and perceived risk are the most important factors in acceptance of human being gene-recombination technology.