两类优化算法在金融市场风险管理模型中的应用研究

发布时间：2018-03-31 04:32

本文选题：Markowitz　切入点：均值-方差模型　出处：《广西大学》2017年硕士论文

【摘要】：在现代金融学领域,证券投资组合问题始终是投资者与相关学者关注的热点问题.现代证券投资组合理论始于1952年,随后在金融市场中得到广泛应用.时至今日,Markowitz模型仍然是现代证券投资组合理论的重要组成部分,但是经典的均值-方差模型的假设条件有些苛刻,对于现实资本市场拟合度偏低.针对上述经典均值-方差理论的不足,本文在原模型的基础上增加管理费这一目标函数进行模型修正,并使用数学优化方法进行模型改进.最后利用杂草入侵算法进行求解,并针对中国沪深两市的股票数据进行实例分析.信用风险是指交易对方违约造成经济损失的风险,是整个金融市场最为古老却一直存在的风险形式之一.随着世界金融市场一体化的推进,中国进一步参与到激烈的国际竞争中,国内金融行业信用风险管理领域面临国内外的双重挑战.本文研究了经典信用风险度量模型—KMV信用风险度量模型,分析了 KMV信用风险模型的基本思想、主要假设、基本参数以及参数求解等问题.提出了 Levenberg-Marquardt方法的下降方向改进方法,给出了改进方法的算法步骤,证明了改进方法的收敛性,给出了收敛次数的论证.针对中国证券市场的现实案例,本文使用改进的算法求解KMV模型,计算得出公司的违约概率,证明了算法的有效性。
[Abstract]:In the field of modern finance, portfolio problem has always been a hot issue for investors and related scholars. The Markowitz model is still an important part of the modern portfolio theory, but the classical mean-variance model is a bit harsh. In view of the deficiency of the classical mean-variance theory mentioned above, this paper increases the objective function of management fee on the basis of the original model and modifies the model. Finally, we use the weed invasion algorithm to solve the problem, and analyze the stock data of Shanghai and Shenzhen stock markets. Credit risk is the risk of economic loss caused by the other party's default. It is one of the oldest but persistent forms of risk in the entire financial market. With the development of the integration of the world's financial markets, China has further participated in the fierce international competition. This paper studies the classical credit risk measurement model-KMV credit risk measurement model, and analyzes the basic ideas and main assumptions of KMV credit risk model. In this paper, the descent direction improvement method of Levenberg-Marquardt method is proposed, the algorithm steps of the improved method are given, and the convergence of the improved method is proved. In this paper, the convergence times are proved, and the improved algorithm is used to solve the KMV model. The probability of default of the company is calculated, and the validity of the algorithm is proved.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

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