一种计算市场最优组合的几何方法

提出了一种通过均值方差有效前沿上计算无风险资产参与组合时的市场最优组合的几何方法。该方法不仅解决了Matlab金融工具箱组合分析函数在实际计算时常常失效的问题，而且考虑了模型的经济意义，提高了计算的鲁棒性。     

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.

     

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.     

以可存品与非可存品为消费对象的最优投资消费决策

传统的投资消费决策问题考虑的消费对象局限于单一的非可存品或者单一的可存品 .而且假定银行的贷款利率等于存款利率 .本文假定银行的贷款利率大于存款利率 ,并且投资者的消费对象为包含可存品与非可存品的组合 .可存品的价格假设服从几何布朗运动 ,它的折旧率假定为一个常值 .应用随机控制方法 ,得到等弹性效用函数情形下的最优投资消费策略的显式表达     

最优证券组合的结构特征研究

在库恩－塔克条件基础上，研究了马尔科维茨理论框架内最优证券组合的结构特征，进－步扩展了关于最优证券组合结构特征和有效边界形状的现有成果。     

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.     

存贷利率不等下具有随机跳跃收入的消费与投资策略

研究贷款利率大于存款利率下具有随机跳跃收入的最优策略,拓展了Merton模型.给出了财富预算方程,运用动态规划原理及随机分析导出该问题的HJB方程,并由此得到一般情形下抽象形式的解.在一类特殊HARA情形下讨论了具有显式反馈形式的最优消费和投资策略.     

基于跳跃扫描误差扩散半色调算法研究

误差扩散算法最早是由Floyd-Steinberg提出,并在当时成为处理效果最好的算法之一。它可以输出视觉效果良好的半色调图像,因而得到了广泛的推广。为改善该传统误差扩散算法均易在中频区域产生结构性纹理现象,提出了一种基于跳跃扫描路径的误差扩散半色调算法。算法在对像素点进行扫描时会根据一定的条件进行跳跃扫描,直接处理若干像素点之后的像素,并将处理后的误差扩散至相邻但还未经处理的像素点上。大量的实验表明,合理的跳跃距离能够帮助有效地抑制半色调图像中的结构性纹理,得到效果更好的半色调图像,具有更深远的意义和实际应用价值。     

市场指数模型下最优证券组合的简化算法

研究市场指数模型下最优证券组合的简化算法,扩展了针对预期超额收益—贝塔比率最大化提出的简化算法,并将其应用于确定最小风险证券组合构成、考虑风险容忍度的最优证券组合构成、允许和不允许限制性卖空情况下有效证券组合构成及其变动。     

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.     

An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.      

基于风险价值约束的动态均值-方差投资组合的研究

研究了基于风险价值约束的动态均值-方差项目投资组合的数学模型,该模型是控制带约束的随机线性二次型（LQ）控制问题.在讨论该随机LQ控制问题的解之后,给出投资组合动态数学模型对应的随机哈密顿-雅克比-贝尔曼方程的解,得出了有效边界和最佳策略,讨论了风险价值约束的影响.最后,针对某油田勘探开发项目的实际情况,应用上述结论求出该实例的解,并讨论了风险价值约束发挥的作用.     

Adaptive Multi-Step Evaluation Design With Stability Guarantee for Discrete-Time Optimal Learning Control

This paper is concerned with a novel integrated multi-step heuristic dynamic programming (MsHDP) algorithm for solving optimal control problems. It is shown that, initialized by the zero cost function, MsHDP can converge to the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Then, the stability of the system is analyzed using control policies generated by MsHDP. Also, a general stability criterion is designed to determine the admissibility of the current control policy. That is, the criterion is applicable not only to traditional value iteration and policy iteration but also to MsHDP. Further, based on the convergence and the stability criterion, the integrated MsHDP algorithm using immature control policies is developed to accelerate learning efficiency greatly. Besides, actor-critic is utilized to implement the integrated MsHDP scheme, where neural networks are used to evaluate and improve the iterative policy as the parameter architecture. Finally, two simulation examples are given to demonstrate that the learning effectiveness of the integrated MsHDP scheme surpasses those of other fixed or integrated methods.     

动态规划最优控制在非线性系统中的应用

应用一种新的自适应动态最优化方法(ADP),在线实现对非线性连续系统的最优控制。首先应用汉密尔顿函数（Hamilton-Jacobi-Bellman, HJB）求解系统的最优控制,并应用神经网络BP算法对汉密尔顿函数中的性能指标进行估计,进而得到非线性连续系统的最优控制。同时引进一种新的自适应算法,基于参数误差,在线实现对系统进行动态最优求解,而且通过李亚普诺夫方法对参数收敛情况也进行详细的分析。最后,用仿真结果来验证所提出的方法的可行性。     

Optimal Synchronization Control of Heterogeneous Asymmetric Input-Constrained Unknown Nonlinear MASs via Reinforcement Learning

The asymmetric input-constrained optimal synchronization problem of heterogeneous unknown nonlinear multiagent systems(MASs) is considered in the paper. Intuitively,a state-space transformation is performed such that satisfaction of symmetric input constraints for the transformed system guarantees satisfaction of asymmetric input constraints for the original system. Then, considering that the leader’s information is not available to every follower, a novel distributed observer is designed to est...     

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton–Jacobi–Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.     

基于梯度估计的非线性系统最优控制及仿真

基于自适应动态规划（ADP）执行-评价结构,应用神经网络（NN）对非线性系统进行最优控制求解.首先提出所求解非线性系统的一般形式;其次给定二次正定性能指标,求其哈密尔顿函（HJB）函数;分别应用神经网络对执行-评价结构中的性能指标和最优控制进行逼近,神经网络权重参数应用梯度法求得,从而可以求得其最有控制策略.而且对执行机构和评价机构神经网络权重参数的收敛性以及系统总体的稳定性进行了详细的分析,证明所求控制策略可以使系统稳定;最后,用仿真结果来验证所提出的方法的可行性.