【作者】 王雨飞；

【导师】 王宇平；

【作者基本信息】 西安电子科技大学 ， 管理科学与工程， 2007， 硕士

【摘要】 风险值(Value-at-Risk, VaR)是一种以统计技术全面度量市场风险的方法,是指在正常的市场环境下,给定一定的时间周期和置信水平,预期最大损失的测度。条件风险值(Conditional Value-at-Risk, CVaR)是指损失额超过VaR部分的期望损失值或平均损失值。它具有VaR模型的优点,同时在理论上又具有良好的性质,如具有次可加性、凸性等。目前,在建立CVaR的数学模型方面有连续型CVaR和离散型CVaR模型,本文主要讨论连续型CVaR,在研究的过程中,运用了系统理论、归纳演绎、比较与实证分析等研究方法。全文共分五章进行。第一章介绍了本文的研究背景,VaR、CVaR和遗传算法的研究概况。第二章概述了VaR模型和CVaR模型,第三章研究连续型单损失CVaR模型及其基于改进遗传算法的解,第四章研究连续型多损失CVaR模型及其基于改进多目标遗传算法的解,第五章对全文进行了总结。本文所取得的研究成果主要有以下几点:1.研究了连续型单损失CVaR模型。通过对线性损失函数的改进,建立了CVaR的一个非线性规划模型,推广了CVaR已有的线性规划模型。通过一种改进的遗传算法求出新的CVaR模型的近似最优解,得到更优的VaR和CVaR值,有效降低了风险。2.研究了连续型多损失CVaR模型,并建立了CVaR的一个多目标优化模型。根据一种新的关系算子,利用求解多目标规划问题的Pareto多目标遗传算法对连续型多损失CVaR模型进行了求解,得到更优的VaR和CVaR值,有效降低了风险。3.利用深证成份股6只股票(深发展、深科技、深万科、世纪星源、深华新和深天地)对新的模型进行了实证分析,通过MATLAB编程进行了数值实验,结果表明对模型和算法的改进是有效的。更多还原

【Abstract】 The value at risk (VaR) is a statistic method to measure the risk of stock markets or portfolio, and the conditional value at risk (CVaR) is another kind of statistic method to measure the risk of portfolio, and it measures the risk by calculating the mean of the values which exceed the VaR. CVaR overcomes several limitations of VaR and has good properties, especially its good computability.The research on CVaR mainly focuses on discrete type of CVaR and continuous type of CVaR. This thesis studies continuous type of CVaR based on the methods of systems theory, induction and deduction, comparison and empirical analysis etc.The thesis is organized as follows. In Chapter 1, we introduce the background and the concepts of VaR, CVaR and genetic algorithms. In Chapter 2, we introduce the research status on VaR and CVaR. In Chapter 3, the continuous type of CVaR model with single loss is studied. In Chapter 4, the continuous type of CVaR model with multiple losses is studied. Chapter 5 concludes the work.The main results obtained in this thesis are as follows.1. The continuous type of CVaR models with single loss is studied. The nonlinear loss functions are designed first. Based on this, a nonlinear programming model for CVaR problem is proposed, which generalized the existing linear CVaR models. Then an improved genetic algorithm is designed to solve the proposed nonlinear programming model. The simulation results indicate the proposed method can decrease the values of both CVaR and VaR.2. The continuous type of CVaR model with multiple losses is studied and a multi-objective optimization model is proposed. To overcome the limitations of traditional multi-objective optimization methods, A Pareto multi-objective genetic algorithm for multi-objective programming problems is used. The proposed model and algorithm can decrease the values of both CVaR and VaR.3. The simulations are made for the proposed algorithms by using some data on Shenzhen更多还原