非定常资产发展方程的最优控制分析

讨论了一类非定常非线性的资产发展方程中资产积累率的最优控制问题,利用泛函分析和积分方程理论,得到了最优解的存在唯一性.     

受环境影响的非定常企业资产发展方程解的性质

将中性技术进步函数与环境制约函数引入资产发展方程中,利用积分方程和泛函分析的理论研究该方程的解的存在唯一性,以及与边界条件相关的性质,这一问题的研究为资产问题的研究提供了理论基础.     

具有劳动力增长的非定常企业投资方程解的性质

将劳动力增长方程引入企业投资方程,以按劳动力计算的人均资产为状态变量,研究该方程的等价方程的解的存在唯一性,并讨论了科技进步对资产增加的重要作用.     

股票收益为双曲分布时的欧式期权定价问题

本文考虑的是股票收益为双曲分布下欧式期权的定价问题，在只有一种无风险资产和一种风险资产的光滑市场上，通过自融资策略，得到权价格所满足的PDE方程，并给出了特定情况下期权价格的显示形式。此外，还从方程的角度说明了股票的波动越大，以期为标的资产的期权价格就越高。     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

一类线性定常资产发展方程的稳定性分析

将中性技术进步函数引入资产发展方程中,利用泛函分析的理论和初值比较、边界比较的方法研究该方程的解的稳定性,并得到了国民生产总值与消费水平的变化趋势,结果可为经济发展问题的研究提供了理论基础.     

固定支出下最优资产组合策略

在固定消费支出水平的条件之下,文章就资产组合问题建立常方差弹性（CEV）模型,应用随机控制原理求出了相应的非线性Hamilton—Jacobi—Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题。通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果．     

Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略

本文研究了Ornstein-Uhlenbeck模型下确定缴费型养老金计划(简称DC计划)的最优投资策略,其中以最大化DC计划参与者终端财富(退休时其账户金额)的CRRA效用为目标.假定投资者可投资于无风险资产和一种风险资产,风险资产的瞬时收益率由Ornstein-Uhlenbeck过程驱动,该过程能反映市场所处的状态.利用随机控制理论,给出了相应的HJB方程与验证定理;并通过求解相应的HJB方程,得到了最优投资策略和最优值函数的解析式.最后分析了瞬时收益率对最优投资策略的影响,发现当市场向良性状态发展时,投资在风险资产上的财富比例呈上升趋势;当初始财富足够大且市场状态不变时,投资在风险资产上的财富比例几乎不受时间的影响.     

考虑交易费用和债务的再保险和投资问题

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题. 假设保险公司本身有着一定的债务, 债务的多少服从线性扩散方程. 保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险. 资产中风险资产的价格波动服从几何布朗运动, 其债务多少的演化也是依据布朗运动而上下波动. 该文考虑了风险资产与债务之间的相互关系, 考虑了在进行风险投资时的交易费用, 并且利用HJB方程求得保险公司的最大最终资产的预期指数效用, 给出了相应的最优价值函数和最优策略的数值解.     

随机双曲折现下的消费与最优投资策略探究

在本文中,我们主要讨论在随机双曲折现中,当投资者的消费行为是一个布朗运动时,其用于投资风险资产的最优投资额.基于汉密尔顿-雅克比-贝尔曼方程计算常数绝对风险厌恶型投资者的效用函数下的最优投资组合,并给出这组方程的近似解.在此基础上,我们分析当消费服从Wiener过程时风险资产投资的一些重要性质,研究消费行为与风险资产投资行为之间的关系.     

The Lyndon property and uniform interpolation over the Grzegorczyk logic

We consider versions of the interpolation property stronger than the Craig interpolation property and prove the Lyndon interpolation property for the Grzegorczyk logic and some of its extensions. We also establish the Lyndon interpolation property for most extensions of the intuitionistic logic with Craig interpolation property. For all modal logics over the Grzegorczyk logic as well as for all superintuitionistic logics, the uniform interpolation property is equivalent to Craig’s property.     

Banach algebras with unique uniform norm

Commutative semisimple Banach algebras that admit exactly one uniform norm (not necessarily complete) are investigated. This unique uniform norm property is completely characterized in terms of each of spectral radius, Silov boundary, set of uniqueness, semisimple norms; and its connection with recently investigated concepts like spectral extension property, multiplicative Hahn Banach extension property and permanent radius are revealed. Several classes of Banach algebras having this property as well as those not having this property are discussed.

     

拓扑分子格中的有限余复盖性质

本文以素理想为基本工具，讨论了拓扑分子格中的有限余复益性质，给出了有限余复益性质的若干等价刻划。证明了关于有限余复盖性质的ＴＨＸＯＨＯＢ乘积定理成立；具有有限余复盖性质的Ｔ２拓扑分子格是Ｔ４的；在一定条件下Ｔ２拓扑分子格中的具有有限余复盖性质的元素是闭元。     

The Effros metric

The concepts of the Effros metric and the Effros property are extended in such a way that a semigroup of surjective self mappings of a bounded metric space (in place of autohomeomorphism group) is used in the definitions. Relations between the Effros property for and -homogeneity are investigated. Special attention is paid to locally connected continua and the class of all continuous mappings between them. It is shown that local absolute retracts, as well as locally connected curves, have the Effros property for , while 2-dimensional locally connected continua do not have this property. A number of questions are asked.     

Confluent operator algebras and the closability property

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.     

SHADOWING,EXPANSIVENESS AND SPECIFICATION FOR C~1-CONSERVATIVE SYSTEMS

We prove that a C~1-generic volume-preserving dynamical system(diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov.Finally,as in[10,27],we prove that the C~1-robustness,within the volume-preserving context,of the expansiveness property and the weak specification property,imply that the dynamical system(diffeomorphism or flow) is Anosov.     

An equivalence theorem on properties A, B for third order differential equations

Differential equations are often classified according to oscillatory/nonoscillatory properties of their solutions as equations having property A or property B. The aim of the paper is to state an equivalence theorem between property A and property B for third order differential equations. Some applications, to linear as well as to nonlinear equations, are given too. Particularly, we give integral criteria ensuring property A or B for nonlinear equations. Our only assumption on nonlinearity is its superlinearity in neighbourhood of infinity, hence our results apply also to Emden-Fowler type equations.The second author wishes to thank C.N.R. of Italy and Grant Agency of Czech Republic (grant 201/96/0410) which made this research possible.     

Continua for which connected partitions are compact

We investigate connected partitions of continua into compacta. In particular, we consider continua with property that every connected partition into compacta is compact. We characterize graphs which have this property as the trees and the simple closed curve. Dendrites are shown to have the property. An example of a nonlocally connected continuum with the property is also given.     

Nearest feasible paths in optimal control problems: Theory,examples, and counterexamples

Many infinite-horizon optimal control problems in management science and economics have optimal paths that approach some stationary level. Often, this path has the property of being the nearest feasible path to the stationary equilibrium. This paper obtains a simple multiplicative characterization for a single-state single-control problem to have this property. By using Green's theorem it is shown that the property is observed as long as the stationary level is sustainable by a feasible control. If not, the property is, in general, shown to be false. The paper concludes with an important theorem which states that even in the case of multiple equilibria, the optimal path is a nearest feasible path to one of them.The author thanks J. Bona for his helpful comments.     

Decidability of the interpolation problem and of related properties in tabular logics

Propositional modal and positive logics are considered as well as extensions of Johansson’s minimal logic. It is proved that basic versions of the interpolation property and of the Beth definability property, and also the Hallden property, are decidable on the class of tabular logics, i.e., logics given by finitely many finite algebras. Algorithms are described for constructing counterexamples to each of the properties mentioned in handling cases where the logic under consideration does not possess the required property.