| 一类控制量非负的新型脉冲随机控制模型 |
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| 引用本文： | 刘晓鹏,刘坤会.一类控制量非负的新型脉冲随机控制模型[J].中国科学：信息科学,2011(11). |
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| 作者姓名： | 刘晓鹏 刘坤会 |
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| 作者单位： | 中国科学院应用数学研究所;北京交通大学理学院; |
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| 基金项目： | 国家自然科学基金(批准号:19671004)资助项目 |
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| 摘 要： | 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.
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| 关 键 词： | 脉冲随机控制 控制量 变分方程 最佳控制 半鞅 |
A new class of impulse stochastic control models with non-negative control quantity |
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| LIU XiaoPeng & LIU KunHui Institute of Applied Mathematics,Chinese Academy of Sciences,Beijing ,China, College of Science,Beijing Jiaotong University,Beijing.A new class of impulse stochastic control models with non-negative control quantity[J].Scientia Sinica Informationis,2011(11). |
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| Authors: | LIU XiaoPeng & LIU KunHui Institute of Applied Mathematics Chinese Academy of Sciences Beijing China College of Science Beijing Jiaotong University Beijing |
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| Affiliation: | LIU XiaoPeng1 & LIU KunHui2 1 Institute of Applied Mathematics,Chinese Academy of Sciences,Beijing 100080,China,2 College of Science,Beijing Jiaotong University,Beijing 100044 |
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| Abstract: | 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 two-variable 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... |
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| Keywords: | impulse stochastic control control quantity variational equation optimal control semi-martingale |
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