As two special types of the general n-dimension fuzzy numbers, fuzzy n-cell numbers and fuzzy n-ellipsoid numbers play an important role in the representations of imprecise multichannel digital information. Denote the families of all n-dimension fuzzy numbers, fuzzy n-cell numbers and fuzzy n-ellipsoid numbers, by K(Rn), L(Rn) and E(Rn), respectively. In this paper, we study the topological structures of the sets L(Rn) and E(Rn) with the topology induced by the supremum metric D∞. Our main result is as follows: for every n>1, there exist homeomorphisms H1,H2:(K(Rn),D∞)→[0,+∞)×ℓ2(c) such that H1(L(Rn),D∞)=H2(E(Rn),D∞)={0}×ℓ2(c), where ℓ2(c) is a non-separable Hilbert space whose weight is the cardinality of the set of all real numbers. As a consequence, the spaces (L(Rn),D∞) and (E(Rn),D∞) are homeomorphic to the Hilbert space ℓ2(c), and hence do not have the fixed point property.
We obtain a complete classification of the structure of finite groups in which every self-centralizing subgroup of non-prime-power order is a TI-subgroup or a subnormal subgroup.
Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants. The recent discovery of the powerful class of zero-determinant strategies in the iterated prisoner's dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. However, strategies in the prisoner's dilemma game are only two strategies. Are there these results for general multi-strategy games? To address this question, the paper develops a theory for zero-determinant strategies for multi-strategy games, with any number of strategies. The analytical results exhibit a similar yet different scenario to the case of two-strategy games. Zero-determinant strategies in iterated prisoner's dilemma can be seen as degenerate case of our results. The results are also applied to the snowdrift game, the hawk-dove game and the chicken game.
By empirical evidences, it is difficult to find a trading strategy with consistently good performance over a long period, and strategies' profitability seem to be varying through time in a cycle fashion. Under the price formation mechanism based on a market-maker with risk aversion to inventory, this paper elaborately detects the crucial factors that affect strategy' profitability with two common trading strategies, i.e. trend following strategy and value investing strategy. We find that the capitals invested in strategies play an important role in limiting self's profits and affecting each other's interactions. Also the market maker's risk aversion to inventory could make positive or negative influences on strategies' profitability. Consistent with empirical evidences, the inverted parabola response of strategy' payoffs to self's capitals is found. This pattern implies the profits that the strategy could bring to its users are limited and originates from the balance between the increasing capitals invested and the decreasing payoffs per capital. Based on the cross influences of the variations in one strategy's capitals on the other's payoffs, the interactions between the two strategies could be prey-predator, symbiosis or competition. In the long time horizon with the two strategies' payoffs reinvestment, the market can spontaneously evolve to the equilibrium where each strategy gains even.
对一类拥有风险资产完美信息的两个内部人在连续时间内竞争的市场模型,引入了半强有效性定价下的信息协议古诺均衡.利用滤波理论和极大值原理,探讨了不同协议下的古诺均衡的存在性,给出了所存在均衡的闭式解,以及相应的期望利润,剩余信息,市场流动参数等市场特征,并证明了最优信息协议古诺均衡的存在唯一性.研究表明,双方在选择交易策略时只能释放部分信息,才能达到古诺均衡以实现正的最大化收益;否则,如果不释放信息或完全释放共同的私有信息,则都不存在这种均衡.
将技术指标引入决策树的构建,并结合Adaboost模型优化,以上证综指为例提出一种交叉验证的股票指数价格涨跌预测模型.基于预测模型构建对时间序列数据的量化择时系统,并评估其策略表现.实证结果表明,本文提出的预测模型精度较高,基于预测模型的量化择时系统有更好的表现,具有较优秀的市场状况识别状态和获得超额收益的能力.该结果为决策树在择时策略中的创新性运用提供参考,为技术指标的创新运用提供新的思路.
在实际金融市场中,投资者的决策往往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,本文建立了基于累积前景理论的非凸投资组合选择模型,并提出了一种基于DC分解原理的ADMM算法.该算法能将本文建立的非凸规划转化成两个易于求解的子问题,同时证明了该算法的迭代序列能收敛到原问题的局部最优点.最后,本文对中国A股股市的实际数据集进行了实证检验,将提出的方法与经典的MV方法以及等权重投资策略进行比较.实验结果表明了本文的投资策略具有更高收益和稳健性.
本文在不确定随机的混合市场环境中,针对绿色投资组合优化问题,建立了具有高阶矩的多目标稀疏模型,提出了一种绿色和非绿色资产混合配置的投资策略.具体地,本文把最近上市且缺乏足够样本信息的绿色资产作为不确定变量,而其他具有足够历史数据的资产作为随机变量进行统一建模.在这样一个混合资产环境下,建立了一个具有基数约束的均值-平均绝对下半偏差-偏度的投资组合优化模型,并采用快速非支配排序遗传算法对模型进行求解.最后,针对提出的模型与算法,对中国沪深股市的实际数据集进行了样本外分析.实证结果表明了本文提出的混合配置策略在Sharpe Ratio方面的优越性.
过度自信包括两类偏见:高估私人信息和低估公共信息精度.在一个有连续统过度自信投资者和随机资产供给的市场中,风险资产的价格是唯一的.一方面,交易量由信息高估驱动;另一方面,价格变动的幅度会受到信息低估的抑制.过度交易的行为带来信号偏见,这降低了投资者的效用.引入一定比例的理性投资者后,市场价格也能达到唯一均衡.理性投资者会强化过度自信投资者的信息偏见,从而促进交易量、提高价格质量、改变效用.在投资者风险厌恶系数较高时,过度自信投资的客观交易效用有可能会超过理性投资.
本文研究一般混合策略空间下三个拥有相同完全信息的内部交易者的行为特征,考虑了风险喜好型,风险中性型,风险厌恶型内部交易者模型的多期均衡解,证明了这三个模型的一般混合策略均衡存在且唯一,并且给出了多期离散均衡解下相应参数所满足的差分方程.
增强型指数追踪是近十年来机构投资者一直使用的指数型基金管理策略,主要通过围绕标的指数的头寸建立追踪组合,并增加对特定风格或个股的倾斜来增加超额收益,兼顾了消极型和积极型管理策略的投资优点.本文针对该问题构建了基于三类矩信息不确定集合上的分布式鲁棒优化模型,并利用半无限对偶理论推导了模型的分布式鲁棒对等式,最终转化成半定规划的形式.最后,利用OR-Library的4个标准数据集进行实证分析.实验结果表明:本文提出的模型不仅可以获得稳定的样本外超额收益,而且具有更强的鲁棒性.
在诸多对内幕交易市场进行研究的论文中,大多是围绕内幕交易者的性质展开分析,但是做市商作为内幕交易市场的交易者之一也在很大程度上影响着市场交易,因此本文基于做市商和内幕交易者同时掌握各自私人信息的基础上,对内幕交易和市场均衡进行了理论分析和数值模拟,并得到唯一的线性均衡模型.本文主要利用反向归纳法证明该模型存在唯一的线性均衡,对该线性均衡进行相关分析发现,内幕交易者的交易量与异质先验信念和信息不对称两部分有关,其中基于信息不对称的交易量总体呈上升趋势.另外,当噪声交易者的交易量满足一定条件时,会出现内幕交易者交易量大于噪声交易者交易量的情况.最后通过对模型进行数值模拟发现,内幕交易者的私有信息会随着交易的进行被逐渐披露,以及市场深度与内幕交易者的交易强度息息相关,并且都处于不稳定的状态.
本文旨在针对带有基数约束的高阶矩投资组合优化模型,设计一种高效的混合启发式求解算法.具体地,首先构建一个带有 ?2正则化的均值-方差-偏度模型,并且提出了一个具有全局收敛性的Cubic-Newton算法.然后,进一步考虑基数约束下的模型求解,提出了一种改进的混合启发式算法,其中适应值的计算嵌入了Cubic-Newton算法,以改善迭代种群的质量.最后,利用OR-Library的6个标准数据集进行实证分析,并以样本外夏普比率,样本内外一致性为评价指标.实验结果表明本文提出方法普遍优于等权重投资策略,均值-方差(MV)投资组合策略以及稀疏均值-方差(SMV)投资组合策略.
By analysing the hyperbolic geometry properties of an extremal function on a real line,Mateljevic have been obtained the Schwarz-Pick lemma of real-valued harmonic function,we give a simple proof of this Schwarz-Pick lemma by using the subordinate principle for real-valued harmonic function on the unit disk.As an application of this Schwarz-Pick lemma,we build a new version of Schwarz-Pick lemma for the gradient of harmonic mappings from the unit disk into itself.Our result is sharpness at the original point and generalizes the corresponding result of Colonna.
基于牛顿迭代法,提出了一种求解非线性方程的修正牛顿迭代法,并证明了该方法是3阶收敛的.最后,通过数值实验对比了常见的其他三种类型的迭代法,说明这类修正牛顿迭代法与传统的牛顿迭代法相比,具有更快的收敛速度,从而进一步证实了该方法的有效性.
研究了 pq(p,q为互不相同的素数)维顶点融合范畴的G-扩张,其中G是有限群,确定出它的所有可能的范畴型,并重点研究了 G是n阶循环群(a>和3次对称群S3时各分支中单对象的分布情况.最后,在G-扩张具有辫子结构时给出了它的完全分类.
主要研究带有三个转移条件的Sturm-Liouville有限谱问题.首先通过构造一类正则的带有三个转移条件的Sturm-Liouville问题,验证其恰有nl个特征值,进而表明带有三个转移条件的Sturm-Liouville问题等价于一类矩阵特征值问题,且其具有相同的特征值.此外,证明了这nl 个特征值在非自共轭边界条件下可位于复平面内任何位置,在自共轭边界条件下可位于实轴上任何位置的结论.分析的关键是判断函数的迭代,运用的主要工具是Rouche定理.
In this paper,we study irrotational incompressible water waves with grav-itation and surface tension in a moving domain,where there is a given moving bottom besides a free upper boundary.The main goal of this paper,using paradifferential cacu-lus,is to paralinearize Zakharov formulation in nonlinear water wave problems.Defining a regularized mapping via Possion kernel to flatten the boundary makes the process of paralinearization more delicate.The paralinearization result makes the nonlinear water wave equations a linear system,which lays a foundation for studying the well-posedness of the water waves with a moving bottom.
针对二维奇异摄动对流扩散方程,在任意网格下给出了经典的迎风有限差分格式.利用二元多项式插值技术,推导出一阶最大范数的后验误差估计,并以此设计了一个自适应网格生成算法.数值实验表明本文构造的自适应移动网格算法是有效的.
WOD(widely orthant dependent)随机变量序列是一类非常宽泛的相依随机变量序列,应用 WOD随机变量序列部分和的Menshov-Rademacher型不等式,结合五段截尾技术,研究得到了同分布WOD随机变量序列的Sung型加权和的最大值矩完全收敛性定理,推广和改进了已有的文献的一些最新结果.作为主要结果的一个应用,同时考虑了基于WOD误差的非参数回归模型中加权估计的完全相合性的结果,并且通过模拟验证了理论结果的有效性.
