On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes

Abstract In this paper, we deal with an optimal control, where the system is driven by a mean-field forward-backward doubly stochastic differential equation with jumps diffusion. We assume that the set of admissible control is convex, and we establish a necessary as well as a sufficient optimality condition for such system.

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Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations

SIAM Journal on Control and Optimization ◽

10.1137/120892477 ◽

2013 ◽

Vol 51 (4) ◽

pp. 2809-2838 ◽

Cited By ~ 129

Author(s):

Jiongmin Yong

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Optimal Control Problems ◽

Mean Field ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Quadratic Optimal Control

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An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2024 ◽

2020 ◽

Vol 28 (1) ◽

pp. 1-18

Author(s):

Dahbia Hafayed ◽

Adel Chala

Keyword(s):

Differential Equation ◽

Optimal Control ◽

Maximum Principle ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Control Problem ◽

Stochastic Differential Equations ◽

Doubly Stochastic ◽

Risk Sensitive ◽

Performance Functional

AbstractIn this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.

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Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

Abstract and Applied Analysis ◽

10.1155/2014/839467 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 4

Author(s):

Hui Min ◽

Ying Peng ◽

Yongli Qin

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Optimal Control Problems ◽

Mean Field ◽

Backward Stochastic Differential Equations ◽

Maximum Principles ◽

Control Problems ◽

Linear Quadratic Optimal Control ◽

Fully Coupled

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

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