基于PID控制器的动态投资组合模型

在投资过程中, 投资者都是在发生亏损或预期发生亏损时才对投资头寸进行调整, 即投资者调整投资组合的目的是保证组合能获得正收益. 基于该思想, 以组合的预期收益率与通过组合要实现的收益率之差作为控制量, 通过PID 控制器动态调整组合中各证券的投资权重, 以实现组合下一期的预期收益率与人们在投资之初确定的收益率相等的目标. 仿真结果表明, 按该模型配置的投资组合的预期收益率能够达到目标收益率.     

萤火虫群优化算法在交易费用证券组合中应用

投资组合问题不存在最优解,只存在有效前沿,投资者要权衡收益率、风险以及约束条件等因素。引入上方收益/下方风险比率,用以描述投资效率,结合人工萤火虫群优化算法不需目标函数的梯度信息等特点,用可行性规则来描述投资组合的均衡问题,在人工萤火虫群优化算法中引入可行性规则,从而实现模拟组合投资。通过对5支、15支和18支股票进行模拟组合投资,在收益率、风险、下方差、单位风险/收益率和单位下方差/收益率等五个指标的比较可看出,人工萤火虫群优化算法能有效用于指导投资决策。     

结束时间不确定的投资组合选择问题建模与模型求解方法

针对结束时间具有不确定性的投资问题,建立以区间风险值(PVaR)度量市场风险的收益最大化投资组合选择模型.PVaR计算的复杂性使得模型难以运用一般优化方法求解,因此提出并证明可以通过求解等效的混合整数规划模型来得到原模型的最优解.利用实际股价数据进行数值实验分析,结果表明,求解混合整数规划模型针对小规模短期投资问题可以快速给出最优投资决策方案.     

状态变化下的连续时间动态投资组合选择

运用两状态隐马尔可夫模型刻画金融资产收益率序列的非线性变化,建立状态变化下的连续时间动态投资组合模型,利用动态规划得到最优投资决策的一般解,使用蒙特卡罗方法模拟投资者的投资决策行为.仿真结果表明:状态变化产生了对冲需求,对冲组合的大小依赖于投资者对市场状态的预期;当风险资产的波动率越小时,投资者状态信念的轻微变化都会引起对冲组合较大幅度的变化;当风险厌恶程度越大时,对冲组合对初始状态信念的变化越不敏感.     

考虑投资者心理特征的模糊投资组合优化模型

投资者在实际金融市场中的决策行为往往会受到主观心理认知的影响.考虑参照依赖、敏感性递减和损失厌恶等影响投资决策的心理特征,研究模糊环境下的投资组合选择问题.首先,假设资产的收益为梯形模糊数,依据前景理论中的价值函数,将组合收益转化为体现投资者心理特征的感知价值;然后,以感知价值的可能性均值最大化和可能性下半方差最小化为目标,建立考虑心理特征的模糊投资组合优化模型;接着,为了有效地求解模型,设计一个多种群遗传算法;最后,通过实例分析表明模型和算法的有效性.结果表明,与传统的遗传算法相比,所设计的多种群遗传算法可更有效地求解模型,考虑心理特征的模糊投资组合优化模型能够提升投资者的满意程度,可为实际的投资活动提供决策支持.     

风险效用投资组合模型的遗传算法求解

给出一个折衷考虑风险最小化和收益最大化的单目标决策方法,以单位风险收益最大化为决策目标建立了投资组合的非线性分式规划模型,考虑到分式规划问题的求解难度,利用遗传算法求解模型,并给出算法步骤。最后,给出了数值算例,结果表明该算法是简单有效的。     

软件项目风险应对措施优选的区间模型及其算法

针对软件项目风险应对计划中风险应对措施的优选问题,提出一种区间优化模型.该模型基于项目视角,以风险应对成本和风险水平最小化为目标,结合考虑风险管理者的风险偏好,选出满意的风险应对措施组合.考虑到风险概率和风险损失等参数难以给出精确值,模型采用区间数来表示风险概率和风险损失信息.针对模型的求解,利用区间数距离定义和区间数排序规则,给出一种迭代求解算法.案例分析表明了该模型和算法的有效性和可操作性.     

组合投资双目标概率准则模型及GASS II算法求解

考虑到中国证券交易的限制规定及现实投资者并非完全理性的决策行为,给出了组合投资收益-损失风险双目标概率准则的整数规划模型。通过证券收益经验分布,应用分层抽样的随机模拟,并结合动态变化算子的遗传算法,构造GASS II遗传模拟混合算法,进行概率准则模型的优化求解。股票相关性由其秩相关系数给出,算法将秩和区间划分相联系,指导分层抽样。GASS II算法能有效刻画收益分布的“高峰厚尾”,激发遗传算法的隐含并行搜索特性,避免早熟现象,提高寻优效率与精度。最后给出了一个投资组合实证分析算例的收益-损失风险有效前沿。     

基于改进粒子群算法的投资组合模型

研究最优化处理资产的实际收益率问题,经典的均值一方差模型对于输入参数过于敏感,不能较好的处理真实世界中的实际收益率问题.为了更好的解决上述问题,建立了一种l∞风险函数的双目标投资组合模型.针对模型中目标函数的不连续性,采用了改进的粒子群优化算法进行求解.改进算法在考虑最优和次优位置的基础上,引入了遗传算法中的交叉操作.在仿真中,运用证券市场中的真实数据分析得出,新模型能够获得比均值一方差模型更小的风险值,同时在实际收益率方面表现更好.     

组合投资双目标概率准则模型及GASS II算法求解

考虑到中国证券交易的限制规定及现实投资者并非完全理性的决策行为，给出了组合投资收益－损失风险双目标概率准则的整数规划模型。通过证券收益经验分布，应用分层抽样的随机模拟，并结合动态变化算子的遗传算法，构造GASS II遗传模拟混合算法，进行概率准则模型的优化求解。股票相关性由其秩相关系数给出，算法将秩和区间划分相联系，指导分层抽样。GASS II算法能有效刻画收益分布的“高峰厚尾”，激发遗传算法的隐含并行搜索特性，避免早熟现象，提高寻优效率与精度。最后给出了一个投资组合实证分析算例的收益－损失风险有效前沿。     

A multiple objective stochastic portfolio selection problem with random Beta

When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported.     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

Multi-period portfolio optimization with linear control policies

This paper is concerned with multi-period sequential decision problems for financial asset allocation. A model is proposed in which periodic optimal portfolio adjustments are determined with the objective of minimizing a cumulative risk measure over the investment horizon, while satisfying portfolio diversity constraints at each period and achieving or exceeding a desired terminal expected wealth target. The proposed solution approach is based on a specific affine parameterization of the recourse policy, which allows us to obtain a sub-optimal but exact and explicit problem formulation in terms of a convex quadratic program.In contrast to the mainstream stochastic programming approach to multi-period optimization, which has the drawback of being computationally intractable, the proposed setup leads to optimization problems that can be solved efficiently with currently available convex quadratic programming solvers, enabling the user to effectively attack multi-stage decision problems with many securities and periods.     

基于粗糙规划的不确定加工时间的并行机调度

针对并行机调度中的不确定工件加工时间,提出用粗糙变量表示不确定量,并由此建立该问题的粗糙期望值规划模型.提出一种应用于调度问题的进化规划算法,改进了针对并行机问题的编码方式和变异方法.采用粗糙模拟的方法计算个体的适应值,即粗糙期望估计值,并加以不同规模的算例进行仿真实验.仿真结果表明,改进进化规划算法得到的解优于遗传算法得到的解.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

Generating effective defined-contribution pension plan using simulation optimization approach

This paper presents an optimization approach to analyze the problems of portfolio selection for long-term investments, taking into consideration the specific target replacement ratio for defined-contribution (DC) pension scheme; the purpose is to generate an effective multi-period asset allocation that reaches an amount matching the target liability at retirement date and reduce the downside risk of the investment. A multi-period asset liability simulation model was used to generate 4000 asset return predictions, and an evolutionary algorithm, evolution strategies, was incorporated into the model to generate multi-period asset allocations under four conditions, considering different weights for measuring the importance of matching the target liability and different periods of downside risk measurement. Computational results showed that the evolutionary algorithm, evolution strategies, is a very robust and effective approach to generate promising asset allocations under all the four cases. In addition, computational results showed that the promising asset allocations revealed valuable information, which is able to help fund managers or investors achieve a higher average investment return or a lower level of volatility under different conditions.     

易腐品多周期闭环物流网络鲁棒优化模型

针对不同周期的易腐品需求与退货不确定性问题,构建了易腐品多周期闭环物流网络,并设计了对应的混合整数线性规划（MILP）模型,以实现最低系统总成本、最佳设施选址以及最优配送车辆运输路径的决策。为有效规避不确定参数的影响,采用基约束鲁棒方法,将模型中的部分清晰约束转换为鲁棒对应式。以上海市果蔬农产品企业为实例,通过遗传算法对模型进行求解。结果表明,相对单周期而言,多周期系统具有动态性、系统成本更低的优点,同时通过不确定预算参数的变化分析,验证了鲁棒模型的可行性与有效性,进而为不确定环境下构建多周期闭环物流网络及降低系统成本提供了借鉴。     

Uncertain programming models for portfolio selection with uncertain returns

In an indeterminacy economic environment, experts’ knowledge about the returns of securities consists of much uncertainty instead of randomness. This paper discusses portfolio selection problem in uncertain environment in which security returns cannot be well reflected by historical data, but can be evaluated by the experts. In the paper, returns of securities are assumed to be given by uncertain variables. According to various decision criteria, the portfolio selection problem in uncertain environment is formulated as expected-variance-chance model and chance-expected-variance model by using the uncertainty programming. Within the framework of uncertainty theory, for the convenience of solving the models, some crisp equivalents are discussed under different conditions. In addition, a hybrid intelligent algorithm is designed in the paper to provide a general method for solving the new models in general cases. At last, two numerical examples are provided to show the performance and applications of the models and algorithm.     

Hybrid multilevel programming with uncertain random parameters

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM–DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg–Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.     

Modelling stock selection using ordered weighted averaging operator

The main objective of stock selection is to select a set of assets in the stock market with high‐expected returns. There are many financial variables that affect the performance of stock firms. This paper proposes a novel linear programming model based on the ordered weighted averaging (OWA) operator for identifying superior stocks without requiring the re‐ordering process. The paper first converts a stock selection problem into a preference voting system by considering two different perspectives: an investor perspective in which the goal is to select stocks with the highest return, and a creditor perspective in which the goal is to maximize the repayment ability. The OWA operator is then used to formulate a linear programming model for identifying superior stocks. The usefulness of the proposed method in this paper is shown through an application in the Tehran stock market.