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。     

GASS II遗传模拟混合智能优化算法

通过对遗传算法算子的行为分析，给出概率动态变化的交叉和变异算子。同时，将遗传算法与随机模拟结合。设计GASS II遗传模拟混合智能优化算法。随机模拟采用缩减方差、加速收敛的分层抽样技术，保证抽样遍布整个搜索空间，突破个体分布“畸形”交叉对遗传算法进化能力的限制，有效发挥遗传算法的隐合并行搜索特性，在发生不成熟收敛时能从当前局部解中跳出，搜索转向具有更高适应度的抽样解，迅速收敛到全局最优解，从而有效避免早熟现象，提高了寻优的效率与精度。Benchmark问题评测结果显示出该算法的有效性。     

GASS Ⅱ遗传模拟混合智能优化算法

通过对遗传算法算子的行为分析,给出概率动态变化的交叉和变异算子.同时,将遗传算法与随机模拟结合,设计GASS Ⅱ遗传模拟混合智能优化算法.随机模拟采用缩减方差、加速收敛的分层抽样技术,保证抽样遍布整个搜索空间,突破个体分布"畸形"交叉对遗传算法进化能力的限制,有效发挥遗传算法的隐合并行搜索特性,在发生不成熟收敛时能从当前局部解中跳出,搜索转向具有更高适应度的抽样解,迅速收敛到全局最优解,从而有效避免早熟现象,提高了寻优的效率与精度.Benchmark问题评测结果显示出该算法的有效性.     

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.     

商业银行贷款组合优化决策的机会准则模型

通过把贷款的收益率刻画为模糊变量,提出了商业银行贷款组合优化决策的机会准则模型,即可能性准则模型、必要性准则模型和可信性准则模型。对于贷款收益率是特殊的三角模糊变量的情况,给出了模型的清晰等价类,这些等价类可以用传统的方法进行求解。对于贷款收益率的隶属函数比较复杂的情况,应用集成模糊模拟、神经网络、遗传算法和同步扰动随机逼近算法的混合优化算法求解模型。数值算例验证了模型和算法的有效性。     

粒子群算法求解组合投资问题

本文在分析概率准则下的组合投资问题模型的基础上,提出了一种基于粒子群优化算法的求解方案,并用C++加以实的收敛性和计算效率,为组合证券投资者提供了一种高效的决策方法。现,然后结合实例,和传统方法、随机模拟结合遗传算法,遗传—禁忌算法等进行比较。证明了文中采用算法具有较高     

求解非规则非致密分布数据的一种算法

考虑到空间数据分布特性差异造成聚类算法采用的不同，在比较分析K均值算法、模糊均值算法和遗传算法的基础上，提出了改进的近邻函数准则，并有机整合形成遗传算法与改进近邻函数准则的新算法，综合了遗传算法的全局性概率搜索的优点，并考虑到空间数据内在的连接方式，在一定程度上较好地解决了数据的非致密非规则分布问题。     

基于模糊理论的最优序贯拍卖策略研究

基于模糊理论,通过将之前拍卖的类似物品回报进行模糊参数化,采用均值—方差对其进行收益和风险的刻画和度量。针对这两个准则提出基于柯布—道格拉斯生产函数的多准则优化函数,进而构建了基于模糊理论的序贯拍卖的顺序策略优化模型;其次,通过集成模糊模拟算法和多准则0-1遗传算法,用于求解该顺序策略优化模型;最后,算例分析比较了五种顺序策略以及优化策略,显示通过模型求解得到的最优策略能够以较低风险取得较高收益。     

一种基于改进免疫遗传算法的证券组合投资策略

针对Markowitz均值-方差模型的不足，结合文献[1]算法提出了一种基于改进免疫遗传算法的证券组合投资策略，它克服了均值一方差模型的收益率必须服从正态分布的局限，并通过将投资收益率、风险损失和风险报酬三者分开度量，明晰了三者的关系。通过引入偏好系数加权法将上述三者进行权衡。仿真结果揭示了风险报酬和风险损失呈线性关系，得到了较好的效果。     

On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision

In this paper, we define the weighted lower and upper possibilistic variances and covariances of fuzzy numbers. We also obtain their many properties similar to variance and covariance in probability theory. On the basis of the weighted lower and upper possibilistic means and variances, we present two new possibilistic portfolio selection models with tolerated risk level and holdings of assets constraints. The conventional probabilistic mean–variance model can be transformed to a linear programming problem under possibility distributions. Finally, an estimation method of possibility distribution is offered and a real example for portfolio selection problem is given to illustrate the usability of the approach and the effectiveness of our methods.     

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.     

基于MIC架构稳健投资组合并行算法及实现

投资组合选择是数量化投资管理领域中的一项关键技术,目前其在应用中亟需高性能算法与实现研究。本论文针对现实投资场景下的稳健投资组合选择最优化模型,设计出高效的并行算法,利用并行计算技术多层级优化性能,实现对稳健投资组合计算的快速响应。该稳健投资组合将模糊集理论与投资组合理论相结合,建立基于可能性理论和机会测度的投资组合模型,用BP神经网络算法和遗传算法对模型进行求解,并在最新的高性能计算集成众核(Many Integrated Core,MIC)架构上实现并行。文章选取上证50指数成份股近两年的交易数据,对并行算法及其性能进行分析。结果显示,该算法计算得到的投资组合收益率优于经典模型收益率和上证50指数同期收益率,基于MIC架构的并行求解性能优于传统的CPU架构,平均并行效率达到80%。     

具有联合椭圆不确定集与概率约束的鲁棒投资组合选择

针对参数在一个联合椭圆不确定集中变化的情形,建立了一个具有概率约束的鲁棒投资组合模型,并将其转化为可由内点算法求解的含线性矩阵不等式(LMI)约束的凸规划问题.应用实际交易数据对所提出的模型进行数值实验和比较,结果表明此模型能够获得具有更好财富增长率的投资策略,并能有效地分散最优投资组合的风险.     

Optimal Control of the Investment Portfolio with Respect to the Quantile Criterion

A two-step problem is considered for the optimal portfolio investment management (control) involving two kinds of securities with respect to the quantile criterion under the assumption of the uniform distribution of the return. The problem with the quantile criterion reduces to optimization of a probability functional, and for the analytical synthesis of an optimal strategy, use is made of a method of dynamic programming. The effectiveness of the suggested strategy in comparison with other known strategies of portfolio control is illustrated by an example.     

Distributionally robust fuzzy project portfolio optimization problem with interactive returns

Effective project selection and staff assignment strategies directly impact organizational profitability. Based on critical value optimization criterion, this paper discusses how uncertainty and interaction impact the project portfolio return and staff allocation. Since the exact possibility distributions of uncertain parameters in practical project portfolio problems are often unavailable, we adopt variable parametric possibility distributions to characterize uncertain model parameters. Furthermore, this paper develops a novel parametric credibilistic optimization method for project portfolio selection problem. According to the structural characteristics of variable parametric possibility distributions, we derive the equivalent analytical expressions of credibility constraints, and turn the original credibilistic project portfolio model into its equivalent nonlinear mixed-integer programming models. To show the advantages of the proposed parametric credibilistic optimization method, some numerical experiments are conducted by setting various values of distribution parameters. The computational results support our arguments by comparing with the optimization method under fixed possibility distributions.     

考虑复杂约束的鲁棒均值-CVaR投资组合模型及粒子群算法

投资组合模型中期望收益等参数的估计误差对最优投资组合策略的稳定性产生重要影响. 在提出考虑复杂约束和交易成本的鲁棒均值-CVaR投资组合模型的基础上, 设计改进粒子群算法来求解该模型. 应用实际交易数据对所提出的模型和算法进行数值实验和比较, 结果表明改进粒子群算法能有效地求解该模型, 产生更稳定的最优投资策略, 从而能够更好地适合实际投资环境.     

分段抽样模型中抽中目标的概率分析

为了增大基于种群操作的搜索技术在有限时间内捕捉到决策空间中的特定目标的概率,基于古典概率模型建立不划分的随机抽样模型和划分成多个子区域的随机抽样模型(简称划分模型),分析比较了两个模型分别进行多次独立随机抽样至少抽中1次特定目标的概率,并证明：当总体中特定目标的数量为1或2时,划分模型抽中特定目标的概率恒大于不划分模型的概率。     

Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events

Importance sampling is a powerful variance reduction technique for rare event simulation, and can be applied to evaluate a portfolio’s Value-at-Risk (VaR). By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importance sampling algorithm to compute the portfolio’s VaR under a multi-variate jump diffusion model. To be more precise, an efficient computational procedure is developed for estimating the portfolio loss probability for those assets with jump risks. And the tilting measure can be separated for the diffusion and the jump part under the assumption of independence. The simulation results show that the efficiency of importance sampling improves over the naive Monte Carlo simulation from 9 to 277 times under various situations.