带有共享不确定参数的鲁棒优化模型

发布时间：2018-01-06 19:27

本文关键词：带有共享不确定参数的鲁棒优化模型　出处：《大连理工大学》2017年博士论文　论文类型：学位论文

【摘要】：本文主要研究目标和约束含有相同不确定参数的优化问题,构建了带有共享不确定参数的鲁棒优化模型,并将模型应用到了投资组合及风险管理等实际问题中.此外,比较了一些古典的投资组合优化模型,研究了它们的最优收益和风险在有效边界上的相对位置.我们首先重述了经典的Markowitz投资组合理论,并且回顾了基于此理论框架构建的均衡收益及风险的投资组合模型和相关的鲁棒优化理论.第二章基于均值-方差模型与Sharpe比率模型,提出了一种新的投资组合模型——方差均值比模型.该模型目标是最小化方差均值比.在解此模型获得的投资策略下,每单位收益所承受的波动最小;并且证明了如果极小化方差均值比最优组合存在,则一定位于均值-方差有效边界上.我们还研究了一些经典的投资组合模型,比较分析了各模型的最优收益和方差,讨论了相应的最优投资组合在有效边界上的相对位置.第三章针目标与约束函数含有相同不确定参数的优化问题,建立了带有共享不确定参数的鲁棒优化模型.即仅已知参数的部分信息时,在满足与参数相关的所有约束下,求解目标函数的"最坏"情况.该类模型的目标和约束函数中参数的最优解取值相同,避免了已有鲁棒模型目标和约束参数的最优解取值不同的缺陷.此外,研究了投资组合问题的带有共享不确定参数的鲁棒风险收益优化模型,并利用对偶定理将模型转化为非线性优化问题.数值实验说明了我们建立的鲁棒优化模型比传统的鲁棒模型更为合理.在相同条件下,当传统的鲁棒模型不可行时,解带有共享不确定参数的鲁棒模型可获得最优投资决策,该决策可为投资者提供指导.第四章研究了带有共享不确定参数的分布鲁棒优化模型.考虑了带有均值绝对标准差约束的极小化风险问题.在仅已知随机收益变量一阶矩、二阶矩的信息下,基于传统的分布鲁棒优化模型,建立了共享不确定参数分布鲁棒优化模型.并利用锥对偶定理将其转化为非线性半定规划问题.通过一个实际的小规模算例说明了所提出模型的合理性以及适用性.第五章研究了管理中的多阶段物流生产与库存问题,此问题目标和约束中同时含有市场需求变量.基于传统的可调节鲁棒优化模型,建立了该问题的共享不确定参数可调节鲁棒优化模型.利用线性对偶定理,可以将模型等价的转化为非凸优化问题.数值实验比较了传统的可调节鲁棒优化模型与共享不确定参数可调节鲁棒优化模型,实验结果表明后者获得的决策在指导投资者进行生产运作方面具有一定的优越性.
[Abstract]:This paper mainly studies the objectives and constraints with the same optimization problem with uncertain parameters, a robust optimization model is constructed with the sharing of uncertain parameters, and the model is applied to the actual problem of portfolio and risk management. In addition, compared with some classical portfolio optimization model, the relative position of the optimal risk and return them in the effective boundary. We first restate the Markowitz portfolio theory, and reviews the theory of robust optimization model of portfolio investment equilibrium return and risk of constructing this theoretical framework and based on the related. The second chapter is based on the mean variance model and Sharpe ratio model, put forward a new portfolio model the mean variance ratio model. The model objective is to minimize the variance to mean ratio. In the solution of this model to obtain the investment strategy, earnings per unit under the wave Minimum; and it is proved that if the minimum variance to mean the optimal combination exists, is located in the efficient frontier of mean variance. We also study the portfolio of some of the classic models, a comparative analysis of the optimal return and variance of each model, discussed the relative position of the corresponding optimal portfolio on the efficient frontier. In the third chapter the goal and the constraint functions with the same optimization problem with uncertain parameters, a robust optimization model for sharing with the uncertain parameters. The information is only known parameters, to meet all the constraints and the related parameters, objective function for solving the "worst". The optimal parameters of objective and constraint functions of the model the solution of the same value, avoid the existing optimal robust model of objective and constraint parameter solution of different values of defects. In addition, the research of the portfolio problem with uncertain parameter sharing Robust optimal risk return model number, and the use of duality theorem to transform the model into a nonlinear optimization problem. Numerical experiments that we establish a robust optimization model is more robust than the traditional model is more reasonable. In the same conditions, when the traditional robust model is not feasible, solutions with shared robust model with uncertain parameters can be obtained the optimal investment decision, the decision can provide guidance for investors. The fourth chapter studies the robust optimization model with shared distribution of uncertain parameters is considered. The mean standard deviation with absolute risk minimization problem in constraint. Only known random return variable first order moment, two order moment information distribution, a robust optimization model based on the traditional, established a shared parameter uncertainty distribution of robust optimization model and using the cone duality theorem into nonlinear semidefinite programming problems. Through a practical small scale The example shows that the proposed model is reasonable and applicable. The fifth chapter studies the production and inventory management in multi stage logistics, the objectives and constraints contained in both market demand variables. Adjustable robust optimization model is established based on the traditional, the problem of shared uncertain robust optimization model parameters can be adjusted. By using the linear duality theorem, equivalent model can be transformed into non convex optimization problems. Numerical experiments adjustable robust optimization model and sharing adjustable robust optimization model with uncertain parameters of the traditional, the experimental results show that the obtained decision for production operation in guiding investors has some advantages.

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F224;F830.59

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