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mean-field stochastic differential equations with a discontinuous diffusion coefficient

Probability, Uncertainty and Quantitative Risk 2023年第3期8卷 351-372页

作者： Jani Nykänen Department of Mathematics and Statistics University of JyväskyläP.O.Box 35FI-40014Finland

We study R^(d)-valued mean-field stochastic differential equations with a diffusion coefficient that varies in a discontinuous manner on the L_(p)-norm of the *** establish the existence of a unique global strong solution in the presence of a robust drift,while also investigating scenarios where the presence of a global solution is not assured.

关键词： mean-field stochastic differential equation Discontinuous diffusion coefficient Existence and nonexistence of strong solutions in L_(p)

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A Nonhomogeneous mean-field Linear-Quadratic Optimal Control Problem and Application

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Acta Mathematicae Applicatae Sinica 2021年第4期37卷 807-819页

作者： Shuang WU College of Science China University of PetroleumQingdao266580China

In this paper,a mean-variance hedging portfolio problem is considered for mean-field stochastic differential *** original problem can be reformulated as a nonhomogeneous linear-quadratic optimal control problem with mean-field *** virtue of the classical completion of squares,the optimal control is obtained in the form of state *** use the theoretical results to the mean-variance hedging portfolio problem and get the optimal portfolio strategy.

关键词： mean-variance hedging portfolio linear-quadratic optimal control problem Riccati equation mean-field stochastic differential equation backward stochastic differential equation

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Optimal vaccination strategy for a mean-field stochastic susceptible-infected-vaccinated system

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International Journal of Biomathematics 2023年第1期16卷 1-27页

作者： Zong Wang Qimin Zhang School of Mathematics and Statistics Ningria University Yinchuan750021P.R.China

The parameters of biological system may change under the influence of different states or state *** change of parameters can also affect the dynamic behaviors of epidemic *** paper presents a mean field stochastic susceptible-infectedvaccinated(SIV)epidemic model which parameters depend on the state *** sufficient and necessary conditions of optimal control of the novel epidemic model are obtained by maximum ***,we perform representative numerical simulations to illustrate the theoretical results and further discuss the feasibility based on the hand,foot and mouth disease(HFMD)data in China.

关键词： mean-field stochastic differential equation stochastic maximum principle SIV epidemic model variational inequality sufficient and necessary conditions.

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mean-field Type Leader-Follower stochastic differential Game with Asymmetric Information

Mean-Field Type Leader-Follower Stochastic Differential Game...

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第32届中国控制与决策会议

作者： Yu Wang School of Control Science and Engineering Shandong University

In this paper,we consider a kind of mean-field type leader-follower stochastic differential game with asymmetric information,where the leader’s information is a sub-σ-algebra of the follower’*** stochastic maximum principle and stochastic filtering technique,we get four Riccati equations and the filtering equation of ***,the Stackelberg equilibrium of feedback form is obtained.

关键词： Asymmetric information leader-follower game mean-field stochastic differential equation open-loop Stackelberg solution stochastic maximum principle

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mean-field stochastic linear quadratic optimal control problems: closed-loop solvability

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Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 37-60页

作者： Xun Li Jingrui Sun Jiongmin Yong Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina Department of Mathematics University of Central FloridaOrlandoFL 32816USA

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost *** coefficients and the weighting matrices in the cost functional are all assumed to be *** strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in *** this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.

关键词： mean-field stochastic differential equation Linear quadratic optimal control Riccati equation Regular solution Closed-loop solvability

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