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.

     

乘性随机离散系统的最优控制

基于对系统随机不确定因素的分析,文中定义了一种新型随机离散系统--乘性随机 离散系统,并研究该类系统的线性二次型(LQ)最优控制问题.首先给出了该类系统的有限时间 和无限时间LQ最优控制律,并着重分析、证明了无限时间LQ最优控制问题的Riccati方程的 正定矩阵解的存在性及相应数值求解算法与收敛性,以及闭环系统的稳定性等问题.仿真结果 表明了该方法的有效性.     

基于策略迭代的连续时间系统的随机线性二次最优控制

针对模型参数部分未知的随机线性连续时间系统, 通过策略迭代算法求解无限时间随机线性二次(LQ) 最优控制问题. 求解随机LQ最优控制问题等价于求随机代数Riccati 方程(SARE) 的解. 首先利用伊藤公式将随机微分方程转化为确定性方程, 通过策略迭代算法给出SARE 的解序列; 然后证明SARE 的解序列收敛到SARE 的解, 而且在迭代过程中系统是均方可镇定的; 最后通过仿真例子表明策略迭代算法的可行性.

     

多阶段均值–方差资产负债管理的随机控制

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值–方差投资组合理论的框架下研究两类资产负债管理模型, 包括带有跨期均值–方差投资目标和带有非破产约束的模型. 由于在动态规划意义下, 方差不具有可分性质, 传统的随机最优控制方法难以直接应用. 如采用处理动态均值–方差优化问题的嵌入法来解决以上问题会带来计算上的困难. 本文借鉴平均场控制的思想对以上两类问题加以研究. 本文假设了非常宽泛的市场模型: 所有的资产都是风险资产; 债务和风险资产之间存在相关性. 在此市场假设模型下, 本文给出了最优投资策略(控制率)的解析表达式和均值–方差有效前沿的表达形式. 本研究成果为投资者提供了新的投资策略, 可应用于更复杂的资产负债管理中.     

基于随机模型预测控制的卫星编队保持方法

针对卫星编队队形保持中存在的随机扰动问题,提出一种基于随机模型预测控制(SMPC)的编队构型保持控制算法。在保证精度的情况下,对非线性相对运动力学方程进行线性化离散处理。考虑到模型预测控制不易处理无界随机扰动的机会约束问题,提出有效解决随机变量信息模糊的分布鲁棒机会约束模型,并通过条件风险价值(CVaR)重构机会约束为可处理约束,得到基于随机模型预测控制的队形保持控制算法。通过计算仿真与传统的模型预测控制算法进行对比,验证了该算法的有效性和优越性。     

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.     

多阶段均值-方差资产负债管理的随机控制（英文）

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值-方差投资组合理论的框架下研究两类资产负债管理模型,包括带有跨期均值-方差投资目标和带有非破产约束的模型.由于在动态规划意义下,方差不具有可分性质,传统的随机最优控制方法难以直接应用.如采用处理动态均值-方差优化问题的嵌入法来解决以上问题会带来计算上的困难.本文借鉴平均场控制的思想对以上两类问题加以研究.本文假设了非常宽泛的市场模型:所有的资产都是风险资产;债务和风险资产之间存在相关性.在此市场假设模型下,本文给出了最优投资策略(控制率)的解析表达式和均值-方差有效前沿的表达形式.本研究成果为投资者提供了新的投资策略,可应用于更复杂的资产负债管理中.     

基于动态规划的资源受限随机工序调度

为解决资源受限条件下的随机工序调度问题,该文提出一种基于离散随机动态系统描述的加工时间离散随机分布且同时具有不兼容和多种可更新资源约束的资源受限项目调度模型,使得在满足资源约束和工序约束的前提下,总的平均加工时间最短。该系统研究了动态规划算法求解该问题的方法。通过实例,验证了该方法的有效性和可行性。     

资源约束项目的改进差分进化参数控制及双向调度算法

针对资源约束项目调度组合优化难题,提出一种改进的动态差分进化参数控制及双向调度算法.通过参数时变衰减与个体优劣评价,自适应控制个体进化参数,提高算法的收敛性能、勘探与开发最优解的能力;基于动态差分进化(Dynamic differential evolution, DDE),提出一种双向调度算法,使用满足任务时序约束的优先数编码、交替正向反向调度,结合标准化编码调整与精英保留的种群随机重建策略,建立了一种高效稳健的双向编码调整机制.通过著名的项目调度问题库(Project scheduling problem library, PSPLIB)中实例集测试,并与其他文献算法比较最优解平均偏差率,验证了所提算法的有效性与优越性.     

强抗扰恒值系统的逆LQ设计

本文着重讨论标量恒值系统在物理约束下的动态抗扰控制问题,提出一种能有效提高系 统动态抗扰能力的控制装置--瞬态补偿器;介绍了一种基于LQ最优控制逆问题的强抗扰 (指在一类外扰作用下动态误差小,且具有输出调节性质)控制器设计方法.通过对一调速系 统的实例研究,表明这种控制器可以大幅度地改善动态速降;无静差且稳定性充裕;物理实验 结果满意.     

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.     

Continuous-time mean–variance portfolio selection with value-at-risk and no-shorting constraints

An investment problem is considered with dynamic mean–variance(M-V) portfolio criterion under discontinuous prices which follow jump–diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton–Jacobi–Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.     

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.     

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.     

Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation

For an investor to claim his wealth resulted from his multiperiod portfolio policy, he has to sustain a possibility of bankruptcy before reaching the end of an investment horizon. Risk control over bankruptcy is thus an indispensable ingredient of optimal dynamic portfolio selection. We propose in this note a generalized mean-variance model via which an optimal investment policy can be generated to help investors not only achieve an optimal return in the sense of a mean-variance tradeoff, but also have a good risk control over bankruptcy. One key difficulty in solving the proposed generalized mean-variance model is the nonseparability in the associated stochastic control problem in the sense of dynamic programming. A solution scheme using embedding is developed in this note to overcome this difficulty and to obtain an analytical optimal portfolio policy.     

Indefinite LQ optimal control for stochastic Takagi–Sugeno fuzzy system under sensor data scheduling: Finite-horizon case

The present paper considers the finite-horizon indefinite linear quadratic (LQ) control problem for stochastic Takagi–Sugeno (T-S) fuzzy systems with input delay. In this paper, we consider the presence of sensor data scheduling, which imposes a communication energy constraint and necessitates optimal state estimation for measurements. Then, by utilizing dynamic programming principles, the stochastic LQ problem under consideration can be solved, while the optimal control policy is developed in terms of the unique solutions to a set of coupled difference Riccati equations (CDREs). Specifically, for simple delay-free case, the linear matrix inequalities based conditions are also proposed, whose feasibility is shown to be equivalent to the well-posedness of the indefinite LQ control under consideration. As an application, our theoretic analysis is extended to study the intermittent observation model caused by random denial-of-service attack.     

Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.