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| 1 | The generalization of a class of impulse stochastic control models of a geometric Brownian motion显示文摘Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls. Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense. | LIU XiaoPeng LIU KunHui | 2009 | Science in China(Series F)2009，52，6： | 6 |
| 2 | A new class of impulse stochastic control models with non-negative control quantity显示文摘This paper advances and studies a new class of impulse stochastic control models. Its state structure is defined by a linear stochastic differential equation of the semi-martingale, its control cost function is a twovariable function of pre-control state quantity and control quantity, and its control quantity is kept non-negative. First this paper constructs a new type of variational equations and proves its solution exists. Using a series of stochastic analysis methods to research the solution function of this type of variational equations, this paper proves the existence of optimal control and analyzes its structure in depth. Because of the big difference between the model in this paper and stochastic control models in previous papers, the analysis method here is quite different from previous ones. It is expected that this paper will have important theoretical significance for stochastic control research, along with wide applicative value in finance control and security management. | LIU XiaoPeng LIU KunHui | 2011 | Science China(Information Sciences)2011，54，3： | 2 |
| 3 | 一类关于几何Brown运动的脉冲随机控制模型之推广显示文摘最近,国际学术界提出了一类关于几何Brown运动的新型随机控制模型,这是一种费用结构与以往不同的重要脉冲控制类型,它在金融控制及投资管理中有着广泛的应用背景和重要的理论意义。文中在相当广泛的条件下对上述随机控制模型进行了实质性地推广并在更加规范的随机过程理论系统下对模型进行了更为精确地描述。通过建立一组适当的变分方程并证明其解的存在性,再应用随机分析的手法,证明了推广后的随机控制模型存在最佳控制。同时,文中还对最佳控制的结构进行了细致地分析。此外,也对变分方程的解函数进行了较为深入地研究,它在某种程度上构成控制模型的值函数。文中所用的分析方法与原文献已有很大的差异,因而在某种程度上来说具有相当的原创性。此外,文中对原文献中分析不太严密的部分给出了严格的证明,使模型的分析和讨论实现了数学意义上的精确化。 | 刘晓鹏 刘坤会 | 2009 | 中国科学(F辑:信息科学)2009，39，11： | 0 |
| 4 | 一类控制量非负的新型脉冲随机控制模型显示文摘提出并研究了一类新型的脉冲随机控制模型,其状态结构由关于半鞅的线性随机微分方程所确定,其控制费用函数为关于控制前状态与控制量的二元函数且其控制量保持非负.首先建立了一类新型的变分方程并证明了其解的存在性.通过对变分方程的解函数进行一系列随机分析处理,证明了最佳控制的存在性且对其结构进行了深入分析.此外,由于本文模型与以往文献中的随机控制模型有着重大差异,因而在分析手法上与以往文献相比颇多差异之处.可以预期,本文不仅在随机控制的研究中将具有重要的理论意义,而且在金融控制及证券管理方面也将有着广泛的应用价值. | 刘晓鹏 刘坤会 | 2011 | 中国科学:信息科学2011，41，11： | 0 |
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