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Mean-Field, Infinite Horizon, Optimal Control of Nonlinear stochastic Delay System Governed by Teugels Martingales Associated with Lévy Processes

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Communications in Mathematics and Statistics 2019年第2期7卷 163-180页

作者： P.Muthukumar R.Deepa Department of Mathematics The Gandhigram Rural Institute(Deemed to be University)GandhigramDindigulTamil Nadu 624302India

This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Lévy processes and standard Brownian motion,in which finite horizon is extended to infinite *** order to describe the interacting many-body system,the expectation values of state processes are added to the concerned ***,sufficient and necessary conditions are established under convexity assumptions of the control ***,an example is given to demonstrate the application of the theory.

关键词： Backward stochastic delay differential equation Infinite horizon Lévy processes Mean-field stochastic maximum principle Teugels martingales

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science China Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 Department of Mathematical Sciences,Huzhou University,Huzhou 313000,China 2 School of Mathematical Sciences,Fudan University,Shanghai 200433,China 1. Department of Mathematical Sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

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.

Optimal Control of Fully Coupled Forward-Backward stochastic Systems with Delay and Noisy Memory 36

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Optimal Control of Fully Coupled Forward-Backward Stochastic...

On the pricing and hedging of precipitation derivatives

第36届中国控制会议

作者： Jinbiao Wu Wencan Wang Yi Peng School of Mathematics and Statistics Central South University Junior Education Department Changsha Normal University

ISBN: (纸本)9781538629185

We study the optimal control of fully coupled forward-backward stochastic systems with delay and noisy memory where the dynamics is governed by a controlled It?-Lévy process and the information available to the controller is possibly less than the overall information. Sufficient and necessary maximum principles for the optimal control of such systems are derived using Malliavin calculus techniques. As an illustration, we apply the result to an optimal consumption problem in a financial model with memory and partial information.

关键词： stochastic Optimal Control Forward-Backward stochastic Systems stochastic maximum principle Noisy Memory Malliavin Calculus

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Probability, Uncertainty and Quantitative Risk 2024年第4期9卷 499-528页

作者： Markus Hess Department of Mechanical and Process Engineering.University of Kaiserslautern-Landau.Gottlicb-Daimler-Straβe 67663 KaiserslauternGermany

In this paper,we present a new precipitation model based on a multi-factor Ornstein-Uhlenbeck approach of pure-jump *** this setup,we derive a representation for the related precipitation swap price process and infer its risk-neutral time *** further deduce a pricing formula for European options written on the prccipitation swap and obtain the minimal variance hedging portfolio in the underlying weather *** the second part of the paper,we provide a precipitation swap price representation under future information modeled by an initially enlarged *** finally derive a formula for the associated information premium and investigate minimal variance hedging of prccipitation dcrivatives undcr futurc information.

关键词： Precipitation model Precipitation swap price Minimal variance hedging.Option pricing Information premium Future information stochastic differential equation Enlarged filtration stochastic maximum principle Malliavin calculus Fourier transform

Optimal control with delayed information flow of systems driven by G-Brownian motion

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Probability, Uncertainty and Quantitative Risk 2018年第1期3卷 229-252页

作者： Francesca Biagini Thilo Meyer-Brandis BerntØksendal Krzysztof Paczka Department of Mathematics LMU MunichTheresienstraße 3980333 MunichGermany Department of Mathematics University of OsloP.O.Box 1053 BlindernN-0316 OsloNorway Department of Mathematics University of MunichTheresienstraße 3980333 MunichGermany

In this paper,we study strongly robust optimal control problems under volatility *** the G-framework,we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongl... 详细信息

关键词： G-Brownian motion optimal control problem stochastic maximum principle

Optimal control of SDEs with expected path constraints and related constrained FBSDEs

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Probability, Uncertainty and Quantitative Risk 2022年第4期7卷 365-384页

作者： Ying Hu Shanjian Tang Zuo Quan Xu University Rennes CNRSIRMAR-UMR 6625F-35000RennesFrance School of Mathematical Sciences Fudan UniversityShanghai 200433China Department of Finance and Control Sciences Fudan UniversityShanghai 200433China Department of Applied Mathematics The Hong Kong Polytechnic UniversityKowloonHong KongChina

In this paper,we consider optimal control of stochastic differential equations subject to an expected path *** stochastic maximum principle is given for a general optimal stochastic control in terms of constrained *** particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the *** the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.

关键词： Optimal stochastic control stochastic maximum principle Expected path constraint Reflected FBSDE

Optimization of Investment, Consumption and Proportional Reinsurance with Model Uncertainty

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Optimization of Investment, Consumption and Proportional Rei...

Mean-Field Type Leader-Follower stochastic Differential Game with Asymmetric Information

第32届中国控制与决策会议

作者： Yuguang Pan School of Control Science and Engineering Shandong University

In this paper, we mainly consider a kind of optimization problem for an insurer including investment,consumption, and proportional reinsurance with model uncertainty. We assume there are only two kinds of assets with a risk-free asset and a risky asset which is a foreign stock. The problem is transformed into a two-person zero-sum differential game of forward-backward stochastic differential equation（FBSDE） first, and then is solved by stochastic maximum principle. Some special cases are considered to give explicit expression of optimal strategy.

关键词： Investment Consumption Reinsurance Model uncertainty stochastic maximum principle

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