Optimality conditions of controlled backward doubly stochastic differential equations

Bahlali, Seid; Gherbal, Boulakhras

doi:10.1515/rose.2010.014

Cited by 15 publications

(24 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that necessary optimality conditions for relaxed controls, where the systems are governed by a stochastic differential equation, were studied by Mezerdi and Bahlali [9] and Bahlali [6], and we note also that necessary optimality conditions for Stochastic controls, where the systems are governed by forward-backward doubly stochastic differential equation, were studied by Bahlali and Gherbal [10] and Han, Peng, and Wu [11].…”

Section: Isrn Applied Mathematicsmentioning

confidence: 75%

On Optimal Control Problem for Backward Stochastic Doubly Systems

Chala

2014

ISRN Applied Mathematics

View full text Add to dashboard Cite

We are going to study an approach of optimal control problems where the state equation is a backward doubly stochastic differential equation, and the set of strict (classical) controls need not be convex and the diffusion coefficient and the generator coefficient depend on the terms control. The main result is necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle.

show abstract

Section: Isrn Applied Mathematicsmentioning

confidence: 75%

On Optimal Control Problem for Backward Stochastic Doubly Systems

Chala

2014

ISRN Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…We suppose that Assumptions 2.2 and 2.4 hold. We may combine the SMP for a risk-neutral controlled differential equation of backward doubly stochastic type from [1,8] with the result of Yong [16] and with aug-mented state dynamics (x, y, z) to derive the adjoint equation. There exist two unique G t -adapted pairs of processes (p 1 , q 1 ) and (p 2 , q 2 ) which solve the following system of backward SDEs:…”

Section: Risk-sensitive Stochastic Maximum Principle Of Backward Doubmentioning

confidence: 99%

“…The idea here is to reformulate in the first step the risk-sensitive control problem in terms of an augmented state process and terminal payoff problem. An intermediate stochastic maximum principle (SMP in short) is then obtained by applying the SMP of [1,8] for a loss functional without running cost; for the same particular cases see [7]. Then we transform the intermediate adjoint processes to a simpler form, using the fact that the set of controls is convex.…”

Section: Introductionmentioning

confidence: 99%

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

Hafayed

Chala

2020

Random Operators and Stochastic Equations

View full text Add to dashboard Cite

In 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.

show abstract

“…Recently, Han et al [7] investigated the necessary condition of optimal controls and obtained a stochastic maximum principle for backward doubly stochastic optimal control systems. Almost simultaneously Bahlali and Gherbal [2] independently proved necessary and sufficient optimality conditions for backward doubly stochastic control systems. Complete information maximum principles of forward-backward doubly stochastic control systems of (1.2) have been studied in [28,29].…”

Section: G (S Y(s) Y (S) Z(s) Z(s)) ← − D B(s)mentioning

confidence: 99%

Partially observed optimal controls of forward-backward doubly stochastic systems

Shi

Zhu

2013

ESAIM: COCV

View full text Add to dashboard Cite

Abstract. The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system. Mathematics Subject Classification. 93E20, 60H10.

show abstract

Optimality conditions of controlled backward doubly stochastic differential equations

Cited by 15 publications

References 23 publications

On Optimal Control Problem for Backward Stochastic Doubly Systems

On Optimal Control Problem for Backward Stochastic Doubly Systems

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

Partially observed optimal controls of forward-backward doubly stochastic systems

Contact Info

Product

Resources

About