A stochastic maximum principle for linear quadratic problem with nonconvex control domain

Ji, Shaolin; Xue, Xiaole

doi:10.3934/mcrf.2019022

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…Also, a generalization of Bellman's principle is presented to control of stochastic systems with more detail by Crespo [4]. Moreover, A Stochastic maximum principle was introduced by Ji [9]. For study of other applications and developments in this area, we refer the readers to [12,13,[15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

2023

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In this paper, we study an optimal control problem in which their cost function is interval-valued. Also, a stochastic differential equation governs their state space. Moreover, we introduce a generalized version of Bellman's optimality principle for the stochastic system with an interval-valued cost function. Also, we obtain the Hamilton-Jacobi-Bellman equations and their control decisions. Two numerical examples happen in finance in which their cost function are interval-valued functions, illustrating the efficiency of the discussed results. The obtained results provide significantly reliable decisions compared to the case where the conventional cost function is applied.

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Section: Introductionmentioning

confidence: 99%

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

2023

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“…Based on the result in Chen, Li and Zhou, 5 Zhou and Li 6 solved the continuous-time mean-variance problem by employing the embedding technique to deal with a stochastic LQ problem. By functional analysis approach and introducing a parameter in the quadratic optimization problem, Ji and Xue 7 first developed a novel stochastic maximum principle to tackle the classical stochastic linear quadratic problem with nonconvex control domain.…”

Section: Introductionmentioning

confidence: 99%

“…We introduce an Hamiltonian function (see (38) in Section 3). It is new, comparing with Ji and Xue, 7 which contains an exponential factor. As an application, we illustrate the effectiveness of the proposed theoretical result by an example.…”

Section: Introductionmentioning

confidence: 99%

A BSDE approach to stochastic linear quadratic control problem

Zhang

2021

Optim Control Appl Methods

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In this article, we study a kind of linear quadratic optimal control problem driven by forward-backward stochastic differential equations (FBSDEs in short) with deterministic coefficients. The cost functional is defined by the solution of FBSDEs. By means of the Girsanov transformation, the original issue is turned equivalently into the classical LQ problem. By functional analysis approach, some necessary and sufficient conditions for the existence of optimal controls have been obtained. Moreover, we investigate the relationship between two groups of first-order and second-order adjoint equations. A new stochastic Riccati equation is derived, which leads to the state feedback form of optimal control. By introducing a new Hamiltonian function with an exponential factor, we establish the stochastic maximum principle to deal with the stochastic linear quadratic problem for forward-backward stochastic system with nonconvex control domain using first-order adjoint equation. An illustrative example is given as well. K E Y W O R D Sforward-backward stochastic differential equations, Hilbert method, maximum principle, stochastic linear quadratic optimal control the literature called a linear quadratic optimal control Problem (LQ problem, in short).

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Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control

Dela

Zheng

2023

J Optim Theory Appl

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In this paper, we discuss a general multidimensional linear convex stochastic control problem with nondifferentiable objective function, control constraints, and random coefficients. We formulate an equivalent dual problem, prove the dual stochastic maximum principle and the relation of the optimal control, optimal state, and adjoint processes between primal and dual problems, and illustrate the usefulness of the dual approach with some examples.

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A stochastic maximum principle for linear quadratic problem with nonconvex control domain

Cited by 3 publications

References 21 publications

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

A BSDE approach to stochastic linear quadratic control problem

Duality Method for Multidimensional Nonsmooth Constrained Linear Convex Stochastic Control

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