A general maximum principle for mean-field forward-backward doubly stochastic differential equations with jumps processes

2019 ◽  
Vol 27 (1) ◽  
pp. 9-25 ◽  
Author(s):  
Dahbia Hafayed ◽  
Adel Chala
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Admissible Control ◽  
Mean Field ◽  
Sufficient Optimality Condition ◽  
Doubly Stochastic

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.

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

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.

scholarly journals Existence of solution for Mean-field Reflected Discontinuous Backward Doubly Stochastic Differential Equation

2020 ◽  
Vol 5 (2) ◽  
pp. 205-216
Author(s):  
Mostapha Abdelouahab Saouli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Mean Field ◽  
Existence Of Solution ◽  
Maximal Solution ◽  
Existence Of A Solution ◽  
Doubly Stochastic

AbstractIn this paper we prove the existence of a solution for mean-field reflected backward doubly stochastic differential equations (MF-RBDSDEs) with one continuous barrier and discontinuous generator (left-continuous). By a comparison theorem establish here for MF-RBDSDEs, we provide a minimal or a maximal solution to MF-RBDSDEs.

scholarly journals A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Shaolin Ji ◽  
Qingmeng Wei ◽  
Xiumin Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Stochastic Differential Equation ◽  
State Constraints ◽  
Terminal State ◽  
Necessary Condition ◽  
Variation Principle ◽  
Linear Quadratic ◽  
Doubly Stochastic

We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.

ON OPTIMAL CONTROL OF A STOCHASTIC EQUATION WITH A FRACTIONAL WIENER PROCESS

2021 ◽  
Vol 6 ◽  
pp. 5-12
Author(s):  
Pavel Knopov ◽  
◽  
Tatyana Pepelyaeva ◽  
Sergey Shpiga ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Existence Theorem ◽  
Wiener Process ◽  
Strong Dependence ◽  
Strong Mixing ◽  
Fractional Wiener Process

In recent years, a new direction of research has emerged in the theory of stochastic differential equations, namely, stochastic differential equations with a fractional Wiener process. This class of processes makes it possible to describe adequately many real phenomena of a stochastic nature in financial mathematics, hydrology, biology, and many other areas. These phenomena are not always described by stochastic systems satisfying the conditions of strong mixing, or weak dependence, but are described by systems with a strong dependence, and this strong dependence is regulated by the so-called Hurst parameter, which is a characteristic of this dependence. In this article, we consider the problem of the existence of an optimal control for a stochastic differential equation with a fractional Wiener process, in which the diffusion coefficient is present, which gives more accurate simulation results. An existence theorem is proved for an optimal control of a process that satisfies the corresponding stochastic differential equation. The main result was obtained using the Girsanov theorem for such processes and the existence theorem for a weak solution for stochastic equations with a fractional Wiener process.

Application of Stochastic Differential Equation and Optimal Control for Engineering Problems

2011 ◽  
Vol 383-390 ◽  
pp. 972-975
Author(s):  
Ramzan Rezaeyan
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Model ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Engineering Problems

Stochastic differential equations(SDEs) is fundamental for the modeling in engineering and science. The goal of this paper is study optimal control of the solution a SDE. We consider the optimal control for risky stocks stochastic model with using of the SDE.

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