鲁棒优化模型在投资组合中的应用研究

发布时间：2018-01-03 02:43

本文关键词：鲁棒优化模型在投资组合中的应用研究　出处：《电子科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：在投资组合决策模型中,最优投资策略对输入参数(如资产的期望收益等)的扰动非常敏感,参数的微小变化可能导致投资决策结果产生非常大的波动。由该类投资组合优化模型产生的最优投资策略在投资组合管理实践中是相当不可靠的。鲁棒优化理论作为一种有效处理参数不确定性的方法引起了学者的关注。相较于传统的将不确定参数假定为随机变量的处理参数不确定方法,鲁棒优化避免了估计随机变量分布的难点,其本质在于将参数的不确定性直接以简单的几何形式(盒状,椭球)描述在模型当中,原规划问题因此转化成为确定的最优化问题,无论参数取不确定范围内的任何值,结果都能一定程度上保证最优。本文将研究鲁棒优化理论在投资组合决策模型中的应用。首先,本文从鲁棒多目标规划角度出发,定义了鲁棒有效解和鲁棒弱有效解,分别构建了盒状不确定集和椭球不确定集下的鲁棒多目标均值-绝对偏差投资组合模型。由于多目标模型通常需要转换成单目标模型进行求解,本文将研究线性加权法(简写为WSS)和?-约束法(简写为ECS)两种标量化方法对鲁棒多目标均值-绝对偏差模型弱有效解的影响。同时本文还研究了鲁棒有效性的损失。其次,本文对鲁棒多目标均值-绝对偏差投资组合模型进行实证分析。比较在具有不同类型的市场、不同时间长度、不同标准差以及不同β指数的条件下,名义投资组合模型和分别在盒状不确定集、椭球不确定集下的鲁棒投资组合模型获得的未来收益表现。结果表明:椭球不确定集在较好描述了参数的不确定性同时,绝大部分情况下能够获得和名义投资组合更接近的解,在最优性和保守性能够取得一定的平衡。同时,鲁棒投资组合策略在未来的收益表现具有一定随机性,但是并不能一定保证高于名义投资组合策略。最后,本文考虑到在实际投资组合中,投资者的决策受到很多现实的限制,如购买量总和、交易所规定的最小购买量、单位最小购买量、投资者的决策偏好、资产种类的数量和交易成本。同时,风险衡量方法近年来也得到迅猛发展,其中之一便是CVaR(条件在险价值)方法。相较于VaR方法,CVaR方法避免了其不满足凸性和次可加性的缺点,能够转化成线性规划。因此,本文考虑构建含有不确定参数和复杂约束的鲁棒均值-CVaR投资组合模型。由于该鲁棒模型属于NP-hard问题,用传统最优化算法存在计算量大和不容易求解的困难,故本文使用智能算法中的粒子群算法进行求解。粒子群算法具有参数设置简单、收敛速度较快、求解容易的特点。同时本文考虑将动态惯性权重、动态加速因子、变异操作等方法来改进基本粒子群算法,避免了其容易出现的早熟收敛,陷入局部最优等缺陷。
[Abstract]:In the portfolio decision model, the optimal investment strategy is very sensitive to the disturbance of input parameters (such as the expected return of assets). The small change of parameters may lead to very large fluctuations in the result of investment decision. The optimal investment strategy generated by this kind of portfolio optimization model is quite unreliable in portfolio management practice. Robust Optimization Theory. As an effective method to deal with parameter uncertainty, scholars have paid close attention to it. Compared with the traditional method, the uncertain parameters are assumed to be random variables. Robust optimization avoids the difficulty of estimating the distribution of random variables, and its essence is to describe the uncertainty of parameters directly in the model in simple geometric form (box, ellipsoid). The original programming problem is thus transformed into a definite optimization problem, regardless of the parameter taking any value within the range of uncertainty. In this paper, we will study the application of robust optimization theory in portfolio decision model. Firstly, this paper starts from the point of view of robust multi-objective programming. Robust efficient solutions and robust weak efficient solutions are defined. The robust multi-objective mean-absolute deviation portfolio models under box-shaped uncertain sets and ellipsoidal uncertain sets are constructed respectively. The multi-objective model usually needs to be transformed into a single-objective model to solve the problem. In this paper, we will study the linear weighting method (WSS) and? The influence of two scalar quantization methods on the weak efficient solution of robust multi-objective mean-absolute deviation model is discussed. The loss of robust validity is also studied. In this paper, the robust multi-objective mean-absolute deviation portfolio model is empirically analyzed and compared under the conditions of different market types, different time lengths, different standard deviations and different 尾 indices. Nominal portfolio model and respectively in the box of uncertainty sets. The future performance of the robust portfolio model under ellipsoidal uncertainty sets. The results show that the ellipsoid uncertainty sets describe the uncertainty of parameters at the same time. In most cases, we can obtain solutions closer to the nominal portfolio, and achieve a certain balance between optimality and conservatism. At the same time, the robust portfolio strategy has a certain randomness in the future income performance. However, it is not guaranteed to be higher than the nominal portfolio strategy. Finally, this paper considers that in the actual portfolio, investors' decisions are limited by a lot of reality, such as the sum of purchases. The minimum purchase amount per unit, the investor's decision preference, the quantity of assets and transaction cost, and the risk measurement methods have been developed rapidly in recent years. One of them is the conditional value at risk (Cvar) method. Compared with the VaR method, the Cvar method avoids the disadvantages of not satisfying convexity and subadditivity and can be transformed into linear programming. In this paper, we consider constructing a robust mean-CVaR portfolio model with uncertain parameters and complex constraints, because the robust model belongs to the NP-hard problem. The traditional optimization algorithm has the difficulty of large computation and difficult to solve, so this paper uses the particle swarm optimization algorithm to solve the problem. The particle swarm optimization algorithm has the advantages of simple parameter setting and fast convergence speed. At the same time, the dynamic inertial weight, dynamic acceleration factor, mutation operation and other methods are considered to improve the basic particle swarm optimization algorithm to avoid its premature convergence. Fall into local optimal defects.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TP18;F830.59

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