Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

Li, Yusong; Zheng, Harry

doi:10.1007/s00245-014-9252-6

Cited by 16 publications

(11 citation statements)

References 32 publications

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“…Then from Theorem 5.2 and Corollary 6.5 in Zhang, Li and Xiong [29], the unique open-loop optimal control of Problem (M-SLQ) ε , for the initial pair (t, x, i), is given by ξ ε kl (s)dÑ kl (s) as in Donnelly and Heunis [5], and Li and Zheng [13], because their filtration is the same, whereÑ kl (s) is defined as follows:…”

Section: Open-loop Solvability: a Perturbation Approachmentioning

confidence: 99%

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Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

Wen

Xiong

2020

Appl Math Optim

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In this paper, we investigate open-loop and weak closed-loop solvabilities of stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. Interestingly, these two solvabilities are equivalent on [0, T ). We first provide an alternative characterization of the open-loop solvability of LQ problem using a perturbation approach. Then, we study the weak closed-loop solvability of LQ problem of Markovian regime switching system, and establish the equivalent relationship between open-loop and weak closed-loop solvabilities. Finally, we present an example to shed on light on finding weak closed-loop optimal strategies within the framework of Markovian regime switching system.

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Section: Open-loop Solvability: a Perturbation Approachmentioning

confidence: 99%

“…Liu, Yin and Zhou [16] considered near-optimal controls of regime switching LQ problems with indefinite control weight costs. Some other recent development concerning regime switching jumps see Donnelly and Heunis [5], and Li and Zheng [13].…”

mentioning

confidence: 99%

Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

Wen

Xiong

2020

Appl Math Optim

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“…The optimal control problem for regime-switching models has received a lot of attention recently, see, for example, [1][2][3][4][5]. There are two existing approaches to solving stochastic optimal control problem in the literature: the dynamic programming and the stochastic maximum principle.…”

Section: Introductionmentioning

confidence: 99%

“…However, when solving the sufficient maximum principle, one of the main assumption is the concavity of the Hamiltonian which may be violated in some applications. In [3], the authors prove a weak sufficient and necessary maximum principle (that does not require concavity assumption) for Markov regime-switching diffusion systems. Let us mention that [5,Theorem 3.1] does not include the cases in which the profit Hamiltonian is not concave (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Let us mention that the latter works do not consider systems of forward-backward stochastic differential equations nor the presence of an external Markov chain in the coefficients of the systems. Using the aforementioned technique, the results obtained in [3,Example 4.7] can be extended to the jump-diffusion case. Our results also generalize the ones derived in [4].…”

Section: Introductionmentioning

confidence: 99%

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Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information

Pamen

2017

J Optim Theory Appl

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This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps. First, a general sufficient maximum principle for optimal control for a system, driven by a Markov regime-switching forward-backward jump-diffusion model, is developed. In the regime-switching case, it might happen that the associated Hamiltonian is not concave and hence the classical maximum principle cannot be applied. Hence, an equivalent type maximum principle is introduced and proved. In view of solving an optimal control problem when the Hamiltonian is not concave, we use a third approach based on Malliavin calculus to derive a general stochastic maximum principle. This approach also enables us to derive an explicit solution of a control problem when the concavity assumption is not satisfied. In addition, the framework we propose allows us to apply our results to solve a recursive utility maximization problem.Keywords Forward-backward stochastic differential equations · Malliavin calculus · Regime switching · Recursive utility maximization · Stochastic maximum principleCommunicated by

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Risk‐sensitive maximum principle for stochastic optimal control of mean‐field type Markov regime‐switching jump‐diffusion systems

Moon

2021

Intl J Robust & Nonlinear

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We consider the risk‐sensitive optimal control problem for mean‐field type Markov regime‐switching jump‐diffusion systems driven by Brownian motions and Poisson jumps with (Markovian) switching coefficients. The system is coupled with its mean‐filed term, that is, the expected value of the state process, and the objective functional is of the risk‐sensitive type. Our problem is closely related to the mean‐field type robust optimization problem for a general class of stochastic jump systems due to the inherent feature of the risk‐sensitive objective functional. By establishing the logarithmic transformations of the associated equivalent singular risk‐neutral control problem, we obtain the risk‐sensitive maximum principle type necessary and sufficient conditions for optimality, where the sufficient condition requires an additional convexity assumption. The risk‐sensitive maximum principle in this article is characterized as the variational inequality, together with the first‐ and second‐order (mean‐field type) adjoint processes as well as the auxiliary first‐order adjoint process. Unlike the risk‐neutral and mean‐field free cases, the additional adjoint equation is induced due to the mean‐field coupling term and the risk‐sensitive logarithmic transformation. We apply the risk‐sensitive maximum principle of this article to the risk‐sensitive linear‐quadratic problem, for which an explicit optimal solution is obtained.

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Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

Cited by 16 publications

References 32 publications

Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information

Risk‐sensitive maximum principle for stochastic optimal control of mean‐field type Markov regime‐switching jump‐diffusion systems

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