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Science China(Information Sciences) 2018年第7期61卷 106-118页

作者： Shuaiqi ZHANG Jie XIONG Xiangdong LIU School of Economics and Commerce Guangdong University of Technology Department of Mathematics University of Macau Department of Mathematics Southern University of Science and Technology Department of Statistics Jinan University

In this article, we consider the partially observed optimal control problem for forward-backward stochastic systems with Markovian regime switching. A stochastic maximum principle for optimal control is developed using a variational method and filtering technique. Our theoretical results are applied to the motivating example of the risk minimization for portfolio selection.

关键词： partial information Markovian regime-switching stochastic maximum principle forwardbackward stochastic differential equation(FBSDE)

stochastic maximum principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance

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Chinese Annals of Mathematics,Series B 2018年第5期39卷 773-790页

作者： Siyu LV Zhen WU School of Mathematics Southeast UniversityNanjing 211189China School of Mathematics Shandong UniversityJinan 250100China

The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.

关键词： stochastic maximum principle Dynamic programming principle Forward-backward stochastic differential equation Regime switching Jump diffusion

stochastic maximum principle for Square-Integrable Optimal Control of Linear stochastic Systems

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Chinese Annals of Mathematics,Series B 2024年第5期45卷 661-676页

作者： Shanjian TANG Xueqi WANG Department of Finance and Control Sciences School of Mathematical SciencesFudan UniversityShanghai 200433China School of Mathematical Sciences Fudan UniversityShanghai 200433China

The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic *** control domain is not necessarily convex and the cost functional can have a quadratic *** particular,they ... 详细信息

关键词： stochastic maximum principle Optimal control Linear stochastic system Square integrability

stochastic maximum principle for systems driven by local martingales with spatial parameters

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Probability, Uncertainty and Quantitative Risk 2021年第3期6卷 213-236页

作者： Jian Song Meng Wang Research Center for Mathematics and Interdisciplinary Sciences Shandong UniversityQingdao 266237ShandongChina School of Mathematics Shandong UniversityJinan 250100ShandongChina

We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial *** the convexity of the control domain,we obtain the stochastic maximum principle as the necessary condition for an optimal control,and we also prove its sufficiency under proper *** stochastic linear quadratic problem in this setting is also discussed.

关键词： stochastic optimal control stochastic maximum principle Local martingale with a spatial parameter

stochastic maximum principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

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Advances in Pure Mathematics 2024年第6期14卷 442-450页

作者： Giuseppina Guatteri Federica Masiero Dipartimento di Matematica Politecnico di Milano via Bonardi Milano Italia Dipartimento di Matematica e Applicazioni Universit di Milano-Bicocca via Cozzi Milano Italia

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

关键词： stochastic Optimal Control Delay Equations Advertisement Models stochastic maximum principle

maximum principle of Optimal stochastic Control with Terminal State Constraint and Its Application in Finance

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Journal of Systems Science & Complexity 2018年第4期31卷 907-926页

作者： ZHUO Yu Department of Finance and Control Sciences School of Mathematical Sciences Fudan University

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.

关键词： Finite-codimensional condition mean-variance portfolio selection problem stochastic maximum principle terminal state constraint.

maximum principle for Partial Observed Zero-Sum stochastic Differential Game of Mean-Field SDEs 36

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Maximum Principle for Partial Observed Zero-Sum Stochastic D...

A Mean-Field Optimal Control for Fully Coupled Forward-Backward stochastic Control Systems with Lévy Processes

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作者： Maoning Tang Qingxin Meng Department of Mathematical Sciences Huzhou University

ISBN: (纸本)9781538629185

In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng（2016）.

关键词： Zero-Sum stochastic Differential Game stochastic maximum principle Partial Observation Open-Loop Saddle Mean-Field

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Journal of Systems Science & Complexity 2022年第1期35卷 205-220页

作者： HUANG Zhen WANG Ying WANG Xiangrong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China.

This paper is concerned with a class of mean-field type stochastic optimal control systems,which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy *** these systems,the coefficients contain not only the state processes but also their marginal distribution,and the cost function is of mean-field type as *** necessary and sufficient conditions for such optimal problems are ***,the applications to the linear quadratic stochastic optimization control problem are investigated.

关键词： Adjoint equation Lévy processes mean-field forward-backward stochastic differential equations stochastic maximum principle Teugels martingales

stochastic LQ Control with Extra Measurability Restriction

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Journal of Systems Science & Complexity 2024年第3期37卷 1003-1022页

作者： WANG Hongxia HU Yuxi LI Zixing SONG Lianfeng College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

Different from the standard linear quadratic(LQ)problem for stochastic systems,the LQ problem considered in the paper has extra measurability *** problem also appears in the LQ control problem for stochastic systems with delays,rational expectations problems,asymmetric information control,and so *** essential difficulty lies in that one has to optimize the input and its conditional expectations *** stochastic maximum principle(SMP)and orthogonal decomposition technique are the key ***,the authors establish the SMP and convert the original problem into forward and backward stochastic difference equations(FBSDEs)with extra measurability ***,the authors resolve the FBSDEs by using the orthogonal decomposition technique and obtain the analytical solution to the underlying ***,the authors explore the essential distinction between the problem and the standard stochastic LQ control ***,numerical examples are given to illustrate the obtained results.

关键词： Multiplicative noise systems optimal control stochastic maximum principle stochastic systems

SINGULAR CONTROL OF stochastic VOLTERRA INTEGRAL EQUATIONS

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Acta Mathematica Scientia 2022年第3期42卷 1003-1017页

作者： Nacira AGRAM Saloua LABED Bernt ФKSENDAL Samia YAKHLEF Department of Mathematics KTH Royal Institute of Technology 10044StockholmSweden University Mohamed Khider of Biskra Algeria Department of Mathematics University of OsloPO Box 1053 BlindernN–0316 OsloNorway

This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort *** total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the *** that it is important to allow the controls to be singular,because in some cases the optimal controls are of this *** Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of *** a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular ***,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.

关键词： stochastic maximum principle stochastic Volterra integral equation singular control backward stochastic Volterra integral equation Hida-Malliavin calculus