The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the con...The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the condition that the cost functional is uniformly convex,the well-posedness of the operator-valued Riccati equation is proved.Based on that,the optimal feedback control of the control problem is given.展开更多
In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this...In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.展开更多
This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)...This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.展开更多
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
基金supported by the National Natural Science Foundation of China(Nos.11971334,12025105)。
文摘The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the condition that the cost functional is uniformly convex,the well-posedness of the operator-valued Riccati equation is proved.Based on that,the optimal feedback control of the control problem is given.
基金financial support partly by the National Nature Science Foundation of China(Grant No.12171053,11701040,11871010&61871058)the Fundamental Research Funds for the Central Universities+2 种基金the Research Funds of Renmin University of China(No.23XNKJ05)the financial support partly by the National Nature Science Foundation of China(Grant No.11871010,11971040)the Fundamental Research Funds for the Central Universities(No.2019XD-A11).
文摘In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.
基金supported by the National Natural Science Foundation of China under Grant Nos.62103442,12326343,62373229the Research Grants Council of the Hong Kong Special Administrative Region,China under Grant Nos.CityU 11213023,11205724+3 种基金the Natural Science Foundation of Shandong Province under Grant No.ZR2021QF080the Taishan Scholar Project of Shandong Province under Grant No.tsqn202408110the Fundamental Research Foundation of the Central Universities under Grant No.23CX06024Athe Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant No.2023KJ061.
文摘This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.
基金This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814904the Natural Science Foundation of China under Grant No. 10671112+1 种基金Shandong Province under Grant No. Z2006A01Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20060422018
文摘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.
