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带Lévy过程的正倒向对偶系统随机控制问题
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作者 冉启康 《纯粹数学与应用数学》 2016年第1期6-13,共8页
讨论了一类控制系统是带Lévy过程的正倒向对偶随机微分方程的随机控制问题.本文假定控制区域为凸集,最优解是使目标函数达到最小的控制过程.使用带Lévy过程的Ito公式及Ekeland变分原理,作者建立了这类随机控制问题极值原理的... 讨论了一类控制系统是带Lévy过程的正倒向对偶随机微分方程的随机控制问题.本文假定控制区域为凸集,最优解是使目标函数达到最小的控制过程.使用带Lévy过程的Ito公式及Ekeland变分原理,作者建立了这类随机控制问题极值原理的一个必要条件. 展开更多
关键词 正倒向对偶随机微分方程 随机控制问题 变分不等式 极值原理 ITO公式
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由布朗运动和列维过程联合驱动的一个有限期的线性二次最优随机控制问题(英文) 被引量:1
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作者 胡世培 贺志民 《应用概率统计》 CSCD 北大核心 2019年第3期275-291,共17页
我们研究了由布朗运动和列维过程联合驱动的线性二次最优随机控制问题.我们利用深刻的截口定理新的仿射随机微分方程存在逆过程.应用拟线性贝尔曼原理和单调迭代收敛方法,我们证明了倒向黎卡提微分方程解的存在性和唯一性.最后,我们证... 我们研究了由布朗运动和列维过程联合驱动的线性二次最优随机控制问题.我们利用深刻的截口定理新的仿射随机微分方程存在逆过程.应用拟线性贝尔曼原理和单调迭代收敛方法,我们证明了倒向黎卡提微分方程解的存在性和唯一性.最后,我们证明了存在一个最优反馈控制且值函数由相应的倒向黎卡提微分方程和相应的伴随方程的初始值合成. 展开更多
关键词 线性二次最优随机控制问题 倒向黎卡提微分方程 列维过程 伴随方程 拟线性迭代方法
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一类部分信息的随机控制问题的极值原理(英文)
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作者 冉启康 《应用数学》 CSCD 北大核心 2009年第2期421-429,共9页
在本文中,我们证明了一类部分信息的随机控制问题的极值原理的一个充分条件和一个必要条件.其中,随机控制问题的控制系统是一个由鞅和Brown运动趋动的随机偏微分方程.
关键词 倒向随机偏微分方程 跳时间 随机最优控制问题 部分信息
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一类随机Riccati矩阵代数方程的线性迭代解法 被引量:1
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作者 王成 朱经浩 《山东理工大学学报(自然科学版)》 CAS 2006年第1期32-35,共4页
针对无穷区间随机线性二次最优控制问题对应的随机代数Riccati方程提出了线性迭代解法.算法中得到Liapunov线性代数方程解的序列,该序列收敛于随机Riccati代数方程的解.已有的理论算法针对该SARE得到的是非线性的常规Riccati代数方程解... 针对无穷区间随机线性二次最优控制问题对应的随机代数Riccati方程提出了线性迭代解法.算法中得到Liapunov线性代数方程解的序列,该序列收敛于随机Riccati代数方程的解.已有的理论算法针对该SARE得到的是非线性的常规Riccati代数方程解的序列,而通常每一次运用经典的Kleinman迭代方法求解常规Riccati代数方程,都是反复迭代求解Lia-punov线性代数方程的过程.这就使得本文算法相较于已有理论算法在针对特定类型SARE时,具有较好的性能. 展开更多
关键词 随机Riccati代数方程(SARE) 常规Riccati代数方程 Liapunov代数方程 随机线性二次最优控制(LQR)问题
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含不动产项目的保险公司再保险-投资策略 被引量:2
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作者 陈树敏 郝志峰 《运筹学学报》 CSCD 北大核心 2018年第1期129-141,共13页
站在保险公司管理者的角度,考虑存在不动产项目投资机会时保险公司的再保险-投资策略问题.假定保险公司可以投资于不动产项目、风险证券和无风险证券,并通过比例再保险控制风险,目标是最小化保险公司破产概率并求得相应最佳策略,包括:... 站在保险公司管理者的角度,考虑存在不动产项目投资机会时保险公司的再保险-投资策略问题.假定保险公司可以投资于不动产项目、风险证券和无风险证券,并通过比例再保险控制风险,目标是最小化保险公司破产概率并求得相应最佳策略,包括:不动产项目投资时机、再保险比例以及投资于风险证券的金额.运用混合随机控制-最优停时方法,得到最优值函数及最佳策略的显式解.结果表明,当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目.进一步的数值算例分析表明:(a)不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系,收益率越高则投资阈值越低;(b)市场环境较好(牛市)时项目的投资阈值降低;反之,当市场环境较差(熊市)时投资阈值提高. 展开更多
关键词 不动产项目 风险投资 比例再保险 破产概率 混合随机控制-最优停时问题
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The State Equations Methods for Stochastic Control Problems
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作者 Lijin Wang Fengshan Bai 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第1期79-96,共18页
The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain a... The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved.Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk.This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems. 展开更多
关键词 Stochastic optimal control Markov chain approximation Euler-Maruyama discretisation midpoint rule predictor-corrector methods portfolio management.
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保险公司实业项目投资策略研究 被引量:6
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作者 陈树敏 李仲飞 《系统科学与数学》 CSCD 北大核心 2010年第10期1293-1303,共11页
考虑保险公司实业项目投资问题.假定1)保险公司可以选择在某一时刻投资一实业项目(Real investment),该项投资可以为保险公司带来稳定的资金收入而不影响其风险;2)保险公司可以将盈余资金投资于证券市场,该市场包含一风险资产.目标是通... 考虑保险公司实业项目投资问题.假定1)保险公司可以选择在某一时刻投资一实业项目(Real investment),该项投资可以为保险公司带来稳定的资金收入而不影响其风险;2)保险公司可以将盈余资金投资于证券市场,该市场包含一风险资产.目标是通过最小化破产概率来确定保险公司实业项目投资时间和风险资产的投资金额.运用混合随机控制-最优停时方法,得到值函数的半显式解,进而得到保险公司的最佳投资策略:以固定金额投资证券市场;当保险公司盈余高于一定额度(称为投资门槛)时进行项目投资,并降低风险资产投资金额.最后采用数值算例分析了不同市场环境下投资门槛与投资金额,投资收益率之间的关系.结果表明:1)项目投资所需金额越少、收益率越高,则项目投资的门槛越低;2)市场环境较好时(牛市)项目的投资门槛提高,保险公司应较多的投资于证券市场;反之,当市场环境较差时(熊市)投资门槛降低,保险公司倾向于实业项目投资. 展开更多
关键词 实业投资 投资门槛 破产概率 混合随机控制-最优停时问题
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H_∞ CONTROL FOR STOCHASTIC SYSTEMS WITH POISSON JUMPS 被引量:4
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作者 Xiangyun LIN Rui ZHANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第4期683-700,共18页
This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including i... This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems. 展开更多
关键词 Externally stable H∞ control internally stable Poisson random measure Riccati equa-tion stochastic system with jumps.
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A Type of General Forward-Backward Stochastic Differential Equations and Applications 被引量:4
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作者 Li CHEN Zhen WU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第2期279-292,共14页
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential... The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained. 展开更多
关键词 Stochastic delayed differential equations Anticipated backward stochastic differential equations Forward-backward stochastic differential equations Linear-quadratic stochastic optimal control with delay Nonzero sum stochastic differential game with delay
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A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lvy Process with Terminal State Constraints 被引量:1
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作者 HUANG Hong WANG Xiangrong LIU Meijuan 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2018年第4期859-874,共16页
This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the ter... This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland's variational principle. Finally, the result is applied to the utility optimization problem in a financial market. 展开更多
关键词 Forward-backward stochastic control system driven by Levy process maximum principle optimal portfolio terminal state constraint.
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STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM WITH LEVY PROCESSES 被引量:7
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作者 Huaibin TANG Zhen WU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2009年第1期122-136,共15页
In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimen... In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations (BSDEs) driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results. 展开更多
关键词 Backward stochastic differential equation generalized stochastic Riccati equation Levy process stochastic linear quadratic optimal control.
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Maximum Principle of Optimal Stochastic Control with Terminal State Constraint and Its Application in Finance 被引量:1
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作者 ZHUO Yu 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2018年第4期907-926,共20页
This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state con... This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland's variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance. 展开更多
关键词 Finite-codimensional condition mean-variance portfolio selection problem stochastic maximum principle terminal state constraint.
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Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations 被引量:1
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作者 Na Li Zhen Wu Zhiyong Yu 《Science China Mathematics》 SCIE CSCD 2018年第3期563-576,共14页
We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of re... We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form. 展开更多
关键词 stochastic linear-quadratic problem Hamiltonian system Riccati equation Poisson process indefinite case
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Constrained LQ Problem with a Random Jump and Application to Portfolio Selection
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作者 Yuchao DONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2018年第5期829-848,共20页
This paper deals with a constrained stochastic linear-quadratic(LQ for short)optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random c... This paper deals with a constrained stochastic linear-quadratic(LQ for short)optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Ito-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations(BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty. 展开更多
关键词 Backward stochastic Riccati equation Default time Mean-varianceproblem
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A Maximum Principle for General Backward Stochastic Differential Equation
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作者 WU Shuang SHU Lan 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2016年第6期1505-1518,共14页
In this paper,the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation.The control domain need not be convex,and the diffusion coefficient c... In this paper,the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation.The control domain need not be convex,and the diffusion coefficient can contain a control variable.The authors obtain a stochastic maximum principle for the optimal control of this problem by virtue of the second-order duality method. 展开更多
关键词 Adjoint equations backward stochastic differential equation maximum principle varia-tional inequality.
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Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion 被引量:2
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作者 BUCKDAHN Rainer JING Shuai 《Science China Mathematics》 SCIE 2014年第10期2025-2042,共18页
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another ... We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case. 展开更多
关键词 fractional Brownian motion stochastic control system backward stochastic differential equation variational inequality maximum principle Girsanov transformation Galtchouk-Kunita-Watanabe decomposition
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H_2/H_∞ CONTROL PROBLEMS OF BACKWARD STOCHASTIC SYSTEMS
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作者 ZHANG Qixia 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第5期899-910,共12页
This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that th... This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations(BSDEs).The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H_2/H_∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H_2/H_∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state. 展开更多
关键词 Backward stochastic differential equations(BSDEs) completion of squares forward backward stochastic differential equations(FBSDEs) H2/H∞ control Riccati equations.
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On Optimal Mean-Field Control Problem of Mean-Field Forward-Backward Stochastic System with Jumps Under Partial Information
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作者 ZHOU Qing REN Yong WU Weixing 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2017年第4期828-856,共29页
This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost function... This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results. 展开更多
关键词 Forward-backward stochastic differential equation Girsanov's theorem jump diffusion Malliavin calculus maximum principle mean-field type partial information.
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Stochastic H_2/H_∞ Control for Poisson Jump-Diffusion Systems 被引量:1
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作者 Meijiao WANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第5期643-664,共22页
This paper is concerned with stochastic H_2/H_∞ control problem for Poisson jump-diffusion systems with(x, u, v)-dependent noise, which are driven by Brownian motion and Poisson random jumps. A stochastic bounded rea... This paper is concerned with stochastic H_2/H_∞ control problem for Poisson jump-diffusion systems with(x, u, v)-dependent noise, which are driven by Brownian motion and Poisson random jumps. A stochastic bounded real lemma(SBRL for short) for Poisson jump-diffusion systems is firstly established, which stands out on its own as a very interesting theoretical problem. Further, sufficient and necessary conditions for the existence of a state feedback H_2/H_∞ control are given based on four coupled matrix Riccati equations. Finally, a discrete approximation algorithm and an example are presented. 展开更多
关键词 Poisson disturbance stochastic Riccati concerned lemma solvability Brownian quadratic attenuation
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