马科维茨均值-方差理论在能源期货投资组合优化中的运用

本文以个人投资者的视角,探索能源期货投资策略。以马科维茨均值-方差理论为依据,以4种能源期货为标的资产,运用MATLAB软件进行计算,构造了区间为第n日至n+252日的动态最佳投资比率策略,以第n+1日至n+253日作为检验区间,并对构造区间、检验区间滚动k次,验证了该投资比率策略的有效性及动态策略的平稳性。投资策略的有效性表明,它是投资者进行能源期货投资的一种可行思路。同时,也验证了马科维茨均值-方差理论可运用于数量较少的能源期货投资组合中。     

基于随机基准的动态均值-方差投资组合选择

在不完全市场下, 研究基于随机基准的动态均值-方差投资组合选择问题. 该问题也可以理解为一个跟踪误差动态投资组合问题, 并将之转化为一个等价的考虑风险调整的期望相对收益最大化问题. 利用随机动态规划方法, 给出了最优投资策略和有效前沿的显式表达式. 最后通过实证分析表明了不完全市场和完全市场下最优投资策略和有效前沿的变化, 并对相关结论进行了经济解释.

     

考虑通货膨胀因素下的连续时间均值-方差投资组合选择

考虑通货膨胀因素,利用均值-方差模型研究连续时间投资组合选择问题.利用 Lagrange 乘子技术将原均值-方差模型转化为一个标准的随机最优控制问题,应用动态规划的方法得到问题的解析解,进而求解出原均值-方差模型的有效投资策略和有效边界的解析表达式.通过实证分析进一步表明了结论的正确性.     

风险资产收益序列相关的多阶段均值-方差投资组合选择

基于多阶段均值-方差框架, 研究任意多种风险资产存在一般收益序列相关时的投资组合选择问题. 首先, 采用Lagrange 对偶原理与动态规划相结合的方法对模型进行求解, 得到多阶段均值-方差模型的有效投资策略和有效边界的解析表达式; 然后, 证明在含有无风险资产的情形下有效边界仍为均值-标准差平面上的一条射线; 最后, 应用所得结论给出一个具体的实例分析.

     

基于均值-方差模型的Relief特征选择优化算法

Relief是公认的效果较好的filter式特征评估方法,但存在特征权值随样本波动的问题,导致识别准确率的下降。提出了一种基于均值-方差模型的特征权值优化算法,采用样本区分能力的平均贡献值的期望和组合贡献值的波动作为特征评估的依据,使得特征选择的结果更加稳定与准确。基于实地采集的地面运动目标的震动信号进行特征选择与分类学习实验,结果表明,该算法得到的特征子集比Relief具有更好的目标区分能力。     

基于DCA-PSO算法的均值-VaR投资组合优化

投资组合决策面临现实证券市场中的大量数据,是一个复杂的组合优化问题,属于NP难问题,传统的算法难以有效求解。文化算法和粒子群算法是新近出现的两种仿生智能算法,将新提出的动态文化粒子群算法用于求解均值-VaR模型,用罚函数方法处理模型中的不等式约束,选取沪市和深市的十六支股票作为备选股票进行实证分析,数值结果表明该算法可以高效、合理地解决投资组合优化问题。     

基于方差约束控制的专家系统故障预测技术研究

基于方差约束控制理论和专家系统的相关知识,研究了动态组合系统内部故障的预测问题。首先根据组合系统的运行情况在线提取故障点在各个子系统的状态观测值,定义了故障点的状态观测均值、误差以及误差和参数结构并进行了分析;然后在给出故障判定定理的基础上,利用专家系统加权算法得到的故障点状态误差和约束容许值,设计了故障预测的流程图;最后根据流程图给出一种新的故障预测算法。理论分析结果表明,这种算法与传统的故障诊断方法和已有的故障预测方法相比有比较明显的优势。     

基于二次粒子群算法的投资组合优化

投资组合优化问题是一个复杂的组合优化问题,属于NP难问题,传统算法很难解决这一问题。将二次粒子群算法应用到投资组合优化问题中,并采用参数的自适应变化。数值模拟表明该算法在投资组合优化问题中能避免陷入局部最优,加快达到全局最优的收敛速度,并在一定意义下优于标准粒子群算法。     

基于随机鲁棒设计的高超音速飞行器线性二次型控制

针对高超音速飞行器具有高度非线性、输入输出之间强耦合以及参数不确定等特点,提出了基于随机鲁棒设计的线性二次型控制。这一控制方案基于系统控制需求,利用蒙特卡罗仿真方法建立随机鲁棒目标函数,并通过遗传算法优化控制系统设计参数。该控制方案保证了飞行的纵向稳定性,改善了其控制性能。基于某常规高超音速飞行器纵向模型进行仿真验证,结果表明该方案能够满足系统控制需求且具有强鲁棒性。     

Efficient implementation of an active set algorithm for large-scale portfolio selection

This paper deals with the efficient implementation of parametric quadratic programming that is specialized for large-scale mean-variance portfolio selection with a dense covariance matrix. The aim is to calculate the whole Pareto front of solutions that represent the trade-off between maximizing expected return and minimizing variance of return.We describe and compare in a uniform framework several techniques to speed up the necessary matrix operations, namely the initial matrix decomposition, the solution process in each iteration, and the matrix updates. Techniques considered include appropriate ordering of the matrix rows and columns, reducing the size of the system of linear equations, and dividing the system into two parts. Regarding implementation, we suggest to simultaneously use two different matrix representations that are specifically adapted to certain parts of the algorithm and propose a technique that prevents algorithm stalling due to numerical errors. Finally, we analyse and compare the runtime of these algorithm variants on a set of benchmark problems. As we demonstrate, the most sophisticated variant is several orders of magnitude faster than the standard implementation on all tested problem instances.     

一类部分信息下带有劳动力收入的最优投资消费问题

最优投资消费问题属于一类典型的随机最优控制问题. 劳动力收入可通过影响期望效用从而影响投资消 费策略的制定. 本文首次在股票收益率和劳动力收入均为不可观测过程情形下, 研究了一类部分信息下的最优投资 消费问题. 首先综合运用Kalman滤波和非线性滤波, 得到了Zakai方程的显式解, 将部分信息下的随机最优控制问题 转化为完备信息下的随机最优控制问题. 其次通过求解HJB方程以及证明验证定理, 得到了该类最优投资消费问题 的最优策略以及值函数的显式表达. 最后采用真实市场数据进行仿真, 对比经典完备信息模型与本文部分信息模型 所得最优策略的差异, 验证了本文所得最优策略在有效利用市场信息方面的优越性.     

Continuous-time safety-first portfolio selection with jump-diffusion processes

This article is concerned with continuous-time portfolio selection based on a safety-first criterion under discontinuous price processes (jump-diffusion processes). The solution of the corresponding Hamilton–Jacobi–Bellman equation of the problem is demonstrated. The analytical solutions are presented when there does not exist any riskless asset. Moreover, the problem is also discussed while there exists one riskless asset.     

Optimal portfolios with regime switching and value-at-risk constraint

We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes.     

跳跃扩散股价的最优投资组合选择

假定股票价格服从跳跃扩散过程.在传统均值-方差组合投资模型基础上,最大化最终收益的期望及最小化最终财富的方差.引进一个随机线性二次最优控制问题作为原问题的近似问题.证明了一个状态为跳跃扩散过程的一般最优控制问题的验证性定理.应用验证性定理求解HJB(Hamilton-Jacobi-Bellman)方程得到了原问题的最优策略.最后还给出了原问题有效前沿的表达式.     

Score-hesitation trade-off and portfolio selection under intuitionistic fuzzy environment

Qualitative portfolio selection approach is a suitable technique for obtaining an optimal portfolio when quantitative data are unavailable and traditional portfolio models are ineffective. However, few studies focus on this issue. This study addresses the lack of research by defining the score-hesitation trade-off rule and introducing the intuitionistic fuzzy set (IFS), based on which an intuitionistic fuzzy portfolio selection (IFPS) model is proposed. The IFS is introduced because of its comprehensive consideration of preference and nonpreference, and is used to represent qualitatively evaluated information from investors and experts. Furthermore, an intuitionistic fuzzy investment scenario is established and a trisection approach is designed to distinguish three types of risk investors, based on which three corresponding IFPS models are constructed. After this, a portfolio selection process under the intuitionistic fuzzy environment is provided, and a simple example is given to show the application of the process. In addition, the investment opportunities and efficient frontier of the IFPS model are investigated to demonstrate the effectiveness of the proposed portfolio selection model. Finally, an example of calculating optimal investment ratios and selecting an optimal portfolio for four newly listed stocks in China is provided to demonstrate the feasibility and practicability of the proposed approaches.     

Mean–variance portfolio selection based on a generalized BNS stochastic volatility model

We study a mean–variance portfolio selection problem via optimal feedback control based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black–Scholes market. The random coefficients of the market are driven by non-Gaussian Ornstein–Uhlenbeck processes that are independent of the underlying multi-dimensional Brownian motion. Our contribution is to explicitly compute and justify optimal portfolios over an admissible set that is large enough to cover some important classes of strategies such as the class of feedback controls of Markov type. Concretely, the mean–variance efficient portfolios and efficient frontiers are explicitly calculated through the method of generalized linear-quadratic control and explicitly constructed solutions to three integro-partial differential equations under a quite mild condition that only requires one stock whose appreciation-rate process is different from the interest-rate process. Related minimum variance issue is also addressed via our main results.     

A class of continuous-time portfolio selection with liability under jump-diffusion processes

A continuous-time mean-variance portfolio selection model is formulated with multiple risky assets and one liability under discontinuous prices which follow jump-diffusion processes in an incomplete market. The correlations between the risky assets and the liability are considered. The corresponding Hamilton–Jacobi–Bellman equation of the problem is presented. The optimal dynamic strategy and the efficient frontier in closed forms are derived explicitly by using stochastic linear-quadratic control technique. Finally, the effects on efficient frontier under the value-at-risk constraint are illustrated.