[计算机]模糊随机变量论文：半方差风险准则与应用.doc

模糊随机变量论文：半方差风险准则与应用【中文摘要】有价证券选择是指投资者把自己的资金按一定比例分别投资在不同种类的证券上,其是通过分散投资,减少亏损,从而获得更高的利润。然而现实生活中受不确定因素的影响,投资收益存在着不确定性。因此,需要采用相应的不确定性理论来研究有价证券选择问题。本文正是基于这种考虑对有价证券选择问题展开研究。本文首先基于模糊随机变量的定义,给出了模糊随机变量半方差的定义,并且推导出三角形和梯形模糊随机变量半方差解析表达式；然后通过模糊随机变量的期望值与半方差两个指标建立了模糊随机环境下的有价证券模型,用所对应的半方差解析公式将原模型转化为等价的随机规划问题。为了验证所提出方法的有效性,本文给出两个数值例子来加以说明。本文的主要工作可以概括为以下四个方面：(1)定义了模糊随机变量的半方差并证明了它的基本性质；(2)利用半方差的定义,导出常见的模糊随机变量的半方差解析表达式；(3)建立有价证券选择模型,基于半方差公式,将模型转化成等价的随机规划问题,从而可以用优化软件进行求解；(4)给出了两个数值例子来说明本文所提出的建模思想及方法的有效性。【英文摘要】Portfolio selection is concerned with the problem that how to allocate investors wealth among alternative securities. The purpose of the investors is to obtain the maximum profit via diversitication of investment. However, the returns of the in-verstments are uncertain in practical market. In this thesis, we employ uncertainty theory to deal with this type of investment problem. Under this consideration, we employ fuzzy random theory to study the portfolio selection problem.According to the definition of fuzzy random variable, we first give the definition of semivariance of fuzzy random variable, and establish the semivariance formulas for triangular and trapezoidal fuzzy random variables. Then, on the basis of expecta-tion and semivariance, we build three classes of portfolio selection models with fuzzy random returns. According to the established semivariance formulas, the original fuzzy random portfolio problems can be reduced to their equivalent stochastic pro-gramming ones, which can be solved by conventional optimization software. Finally, we give two numerical examples to demonstrate the proposed modeling idea.The main contribution of this thesis contains the following four aspects:() The conception of semivariance of fuzzy random variables is defined and its properties are discussed; () The semivariance formulas for fuzzy random variables are deduced; () On the basis of expectation and semivariance, three new classes of portfolio models are esstablished, and the equivalent stochastic models are discussed; () Two numerical examples are provided to demonstrate the proposed modeling idea.【关键词】模糊随机变量 风险 收敛性 期望值 半方差 有价证券选择【英文关键词】fuzzy random variable risk convergence expected value semi-variance portfolio selection【目录】半方差风险准则与应用摘要5-6Abstract6第1章 绪论8-111.1 问题的提出及研究现状8-91.2 论文的结构安排9-11第2章 预备知识11-13第3章 常见的模糊随机变量的半方差计算方法13-253.1 模糊随机变量的半方差定义与性质13-143.2 三角的模糊随机变量的半方差14-183.3 梯型的模糊随机变量的半方差18-25第4章 一般的模糊随机变量的逼近方法25-274.1 模糊随机变量的逼近方法25-264.2 逼近方法关于方差、半方差的收敛性26-27第5章 半方差的应用27-415.1 基于